openapi: 3.0.0
info:
title: Prime Numbers API
description: "# [Prime-numbers-API ](https://prime-numbers-api.com)\n\nWelcome to Prime Numbers API (https://prime-numbers-api.com), the largest commercial database of prime numbers in the world!\n\nHere we have more than __5 billion__ curated primes from the first __130 billion composite numbers__, and counting!\n\n\n\n### [Overview](https://prime-numbers-api.com/index.php?route=journal3/blog)\nWhether you're a scientist, security expert, or you simply love math, Prime Numbers has something to offer you!\n\nIn the last 3 and a half years, we've invested over 1 500 human-hours, over 50 000 computer-hours, with an average processing speed of 4 300 composite numbers per second while using 100% green energy. We've taken the leg work out of finding primes, so you can focus on using them.\n\nWe've also translated the output into 8 of the most commonly used languages, including __Mandarin__, __Hindi__, __Spanish__, __French__, __German__, __Italian__, __Japanese__, and __Russian__, making the Prime Numbers the most accessible API for finding prime numbers in the world!\n\nIf you’re looking for help with encryption, gain access to our __exclusive isolated primes endpoint__ and you can filter for rare primes that lie at least 200, and even up to 500+ numbers away from their closest neighbors! The average probability of finding one of the isolated prime numbers by accident is 1 in over 800,000 (or 0.000124565509%)! The chances of being struck by lightning are 1 in 500,000! Now that’s a strong password!\n\nOur API conveniently translates the language of your smart devices. Every number is returned with its respective translation into binary, senary, and hexa values.\n\nFurthermore, each prime number you receive from the API is home-grown, curated, and 100% genuine; and it even comes with its very own __birth certificate__! No copies, clones, or placeholders here! \n\nThe API results have a multitude of configurations. These range from simple and fast to incredibly verbose, with extensive explanations for each field. Whether you're looking for efficient server-to-server communication or you're in need of prime numbers for educational or research purposes, the results can be custom-tailored to suit your needs!\n\nWith these prime types outputs, you can determine:\n* __Isolated__: rare prime numbers with an average density of 0.000124565509% that are 200 to 500+ composite numbers away from each of their neighbours\n* __Palindromes__: primes which reads the same backwards as forwards (examples: 101, 373, 919)\n* __Twins__: primes that are no more than 2 composite numbers from each other (examples: (5, 7), (11, 13), (17, 19))\n* __Cousins__: primes that are no more than 4 composite numbers from each other (examples: (7, 11), (37, 41), (43, 47))\n* __Sexys__: primes that are no more than 6 composite numbers from each other (examples: (7,13), (13,19), (23,29))\n* __Reversibles__: primes that become a different prime when their decimal digits are reversed (examples: 37, 107, 149)\n* __Pandigitals__: primes in a base has at least one instance of each base digit (examples: 2143 (base 4), 7654321 (base 7))\n* __Repunits__: primes are positive integers in which every digit is one (examples: 11, 1111111111111111111)\n* __Mersenne__: primes that is of the form 2n - 1 (one less than a power of two) for some integer n (examples: 3 (2^2 - 1), 7 (2^3 - 1), 31 (2^5 - 1) )\n* __Fibonacci__: primes that are also Fibonacci numbers (examples: 89, 233, 1597)\n* __Prime type densities__: how many prime type numbers in percentage can be found in every million composite numbers\n* ...and so much more!\n \n\nWhether you're just looking for efficient server-to-server communication, or you're in need of prime numbers for educational or research purposes, the results can be custom tailored to suit your needs!\n\n\n## [API Price Plans](https://prime-numbers-api.com) (https://prime-numbers-api.com)\n| API Plan Name | Free | Maths is Fun | Scientist | Expert |\n|-------------------------------------|---------------------------|---------------------------|---------------------------|---------------------------|\n| Price / month | $0.00 | $7.99 | $19.99 | $29.99 |\n| Summary | Ideal for Maths Enthusiasts or for an opportunity to test drive the system for free | Ideal for Maths Enthusiasts and Educators alike. | Ideal for Big Data, Machine Learning, Artificial Intelligence, Robotics and Internet of Things Scientists as well as for Web and App Developers. | Ideal for System Administrators and Security Experts. |\n| FREE API Key refresh | Automatically, 1st of every month \t | When you need it | When you need it | When you need it \n| Max calls limits | | | | |\n| Maximum calls per day | 100 | 1 000 | 3 000 | 5 000 |\n| Maximum calls per second | 1 | 3 | 5 | 10 |\n| API Endpoints Available | | | | |\n| get-random-prime | included | included | included | included |\n| is-this-number-prime | included | included | included | included |\n| prospect-primes-between-two-numbers | x | included | included | included |\n| get-all-primes-between-two-numbers | x | x | included | included |\n| get-isolated-random-prime | x | x | x | included |\n| Support availability | | | | |\n| Help Centre | included | included | included | included |\n| Support Tickets | x | included | included | included |\n\n\n### [Authentication](https://prime-numbers-api.com/index.php?route=journal3/blog)\nAuthenticate using the API key with extra security provided by the domain name and IP address locks (the API requests are only accepted from your IP or domain name)\n\n\n\n\n### [Status Codes](https://prime-numbers-api.com/index.php?route=journal3/blog)\n* 200 OK\n* 403 user not found\n* 404 no results found\n\n\n\n\n### [Rate limits](https://prime-numbers-api.com/index.php?route=journal3/blog)\n* Maximum calls per second: 1\n* Maximum calls per day: 100\n\n\n\n\n### [Output Format](https://prime-numbers-api.com/index.php?route=journal3/blog)\n* JSON\n\n___\n\n\n### [Usefull Links](https://prime-numbers-api.com/index.php?route=journal3/blog)\n\n* Full documentation: https://prime-numbers-api.com/index.php?route=journal3/blog\n* Swagger OpenAPI: https://swagger.prime-numbers-api.com/\n* Download Swagger YML file: https://swagger.prime-numbers-api.com/prime-numbers.io_open_api_collection.yml\n* Download Postman Collection: http://prime-numbers-api.com/downloads/prime-numbers-api.postman_collection.json\n* Download Postman Environment: http://prime-numbers-api.com/downloads/prime-numbers.io.postman_environment.json\n* Frequently Asked Questions: https://prime-numbers-api.com/index.php?route=information/information&information_id=7\n* Help Centre: http://help.prime-numbers-api.com/\n___\n\n### Other Prime-numbers-API code examples\n* jQuery: https://github.com/Prime-Numbers-API/jquery-example\n* JavaScript Fetch: https://github.com/Prime-Numbers-API/javascript-fetch-example\n* React: https://github.com/Prime-Numbers-API/react-example\n* NodeJS: https://github.com/Prime-Numbers-API/node-example\n* Python: https://github.com/Prime-Numbers-API/python-example\n* PHP: https://github.com/Prime-Numbers-API/php-example\n* WordPress Plugin: https://github.com/Prime-Numbers-API/wordpress-plugin-example\n* Java: https://github.com/Prime-Numbers-API/java-example\n* C: https://github.com/Prime-Numbers-API/c-example"
version: 1.0.0
servers:
- url: https://api.prime-numbers.io
components:
securitySchemes:
apikeyAuth:
type: http
scheme: apikey
security:
- apikeyAuth: []
paths:
/get-random-prime.php:
get:
tags:
- General
summary: get-random-prime (free)
parameters:
- name: key
in: query
schema:
type: string
description: (Required) your API key
example: '{{apiKey}}'
- name: include_explanations
in: query
schema:
type: string
description: >-
includes the full explanations for each item if true (default is
false)
example:
- name: include_prime_types_list
in: query
schema:
type: string
description: >-
includes the full prime types list for each item if true (default is
false)
example:
- name: language
in: query
schema:
type: string
description: >-
show the output translated into that language (it can be english,
mandarin, hindi, spanish, french, german, italian, japanese,
russian) (default is english)
example:
responses:
'200':
description: OK
headers:
Date:
schema:
type: string
example: Tue, 21 Sep 2021 22:29:20 GMT
Server:
schema:
type: string
example: Apache
Access-Control-Allow-Origin:
schema:
type: string
example: '*'
Keep-Alive:
schema:
type: string
example: timeout=5, max=100
Connection:
schema:
type: string
example: Keep-Alive
Transfer-Encoding:
schema:
type: string
example: chunked
Content-Type:
schema:
type: string
example: application/json
content:
application/json:
schema:
type: object
examples:
example-0:
summary: success (no query params)
value:
random_prime_number_value: 3789360173
base_conversions:
binary_value: '11100001110111010000110000101101'
senary_value: '1424003050045'
hexa_value: e1dd0c2d
previous_prime_gap: 52
prime_density: '4.53580000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '4.53580000'
birth_certificate: >-
2018-09-12 20:46:33: server mac-server processed 61 558
computations in 2.5649074642855 micro-seconds using 2 x 3
GHz Quad-Core Intel Xeon CPUs
example-1:
summary: success (with explanations and prime_types)
value:
random_prime_number_value: 48740297191
base_conversions:
binary_value: '101101011001001001011110100111100111'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '34220241420011'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: b5925e9e7
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 8
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '4.05220000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 48 740 000 000 and 48 741 000
000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '4.05220000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated prime
number in this million composite numbers (between 48 740
000 000 and 48 741 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples: 2,
3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373,
383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.00000000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 48 740 000 000
and 48 741 000 000)
is_twin: 'false'
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '0.43520000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 48 740 000 000 and 48
741 000 000)
is_cousin: 'false'
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '0.43820000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 48 740 000 000 and 48
741 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17), (13,19),
(17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '0.77130000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 48 740 000 000 and 48
741 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their decimal
digits are reversed. The name emirp is obtained by
reversing the word prime (examples: 13, 17, 31, 37, 71,
73, 79, 97, 107, 113, 149, 157) (reference:
https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '0.00000000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 48 740 000 000
and 48 741 000 000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance of
each base digit. (examples: 2143 (base 4), 7654321 (base
7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00000000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 48 740 000 000
and 48 741 000 000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00000000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in this
million composite numbers (between 48 740 000 000 and 48
741 000 000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form 2n
- 1 (one less than a power of two) for some integer n.
They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00000000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in this
million composite numbers (between 48 740 000 000 and 48
741 000 000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers (examples:
2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00000000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 48 740 000 000
and 48 741 000 000)
birth_certificate: >-
2020-05-13 00:03:02: server tolo processed 220 772
computations in 10.035093092236 micro-seconds using 2 x
2.2GHz Penta-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
'403':
description: Forbidden
headers:
Date:
schema:
type: string
example: Tue, 21 Sep 2021 22:29:54 GMT
Server:
schema:
type: string
example: Apache
Access-Control-Allow-Origin:
schema:
type: string
example: '*'
X-PHP-Response-Code:
schema:
type: integer
example: '403'
Keep-Alive:
schema:
type: string
example: timeout=5, max=100
Connection:
schema:
type: string
example: Keep-Alive
Transfer-Encoding:
schema:
type: string
example: chunked
Content-Type:
schema:
type: string
example: application/json
content:
application/json:
schema:
type: object
example:
error: please include the api key in your query
/is-this-number-prime.php:
get:
tags:
- General
summary: is-this-number-prime (free)
parameters:
- name: key
in: query
schema:
type: string
description: (Required) your API key
example: '{{apiKey}}'
- name: number
in: query
schema:
type: string
description: >-
(Required) enter a number to check if it is prime or composite
(between 1 and 10^12).
example:
- name: include_explanations
in: query
schema:
type: string
description: >-
includes the full explanations for each item if true (default is
false)
example:
- name: include_prime_types_list
in: query
schema:
type: string
description: >-
includes the full prime types list for each item if true (default is
false)
example:
- name: language
in: query
schema:
type: string
description: >-
show the output translated into that language (it can be english,
mandarin, hindi, spanish, french, german, italian, japanese,
russian) (default is english)
example:
responses:
'200':
description: OK
headers:
Date:
schema:
type: string
example: Tue, 21 Sep 2021 22:24:27 GMT
Server:
schema:
type: string
example: Apache
Access-Control-Allow-Origin:
schema:
type: string
example: '*'
Keep-Alive:
schema:
type: string
example: timeout=5, max=100
Connection:
schema:
type: string
example: Keep-Alive
Transfer-Encoding:
schema:
type: string
example: chunked
Content-Type:
schema:
type: string
example: application/json
content:
application/json:
schema:
type: object
examples:
example-0:
summary: error (prime number no divisors over 100 mil)
value:
target_number: 100000001
is_prime: 'false'
all_divisors: the list of divisors is only available for numbers < 10^8
example-1:
summary: success (check composite number)
value:
target_number: 99909999
is_prime: 'false'
all_divisors: >-
1 3 7 9 19 21 23 57 63 69 133 161 171 191 207 361 399 437
483 573 1083 1197 1311 1337 1449 1719 2527 3059 3249 3629
3933 4011 4393 7581 8303 9177 10887 12033 13179 22743
24909 25403 27531 30751 32661 39537 58121 68951 74727
76209 83467 92253 174363 206853 228627 250401 276759
482657 523089 584269 620559 751203 1447971 1585873 1752807
4343913 4757619 5258421 11101111 14272857 33303333
99909999
example-2:
summary: success (check prime number)
value:
target_number: 41
is_prime: 'true'
all_divisors: '1 41 '
base_conversions:
binary_value: '101001'
senary_value: '105'
hexa_value: '29'
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 6
computations in 0.00026679684322637 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
'403':
description: Forbidden
headers:
Date:
schema:
type: string
example: Tue, 21 Sep 2021 22:23:23 GMT
Server:
schema:
type: string
example: Apache
Access-Control-Allow-Origin:
schema:
type: string
example: '*'
X-PHP-Response-Code:
schema:
type: integer
example: '403'
Keep-Alive:
schema:
type: string
example: timeout=5, max=100
Connection:
schema:
type: string
example: Keep-Alive
Transfer-Encoding:
schema:
type: string
example: chunked
Content-Type:
schema:
type: string
example: application/json
content:
application/json:
schema:
type: object
example:
error: please include the api key in your query
'404':
description: Not Found
headers:
Date:
schema:
type: string
example: Tue, 21 Sep 2021 22:24:11 GMT
Server:
schema:
type: string
example: Apache
Access-Control-Allow-Origin:
schema:
type: string
example: '*'
X-PHP-Response-Code:
schema:
type: integer
example: '404'
Keep-Alive:
schema:
type: string
example: timeout=5, max=100
Connection:
schema:
type: string
example: Keep-Alive
Transfer-Encoding:
schema:
type: string
example: chunked
Content-Type:
schema:
type: string
example: application/json
content:
application/json:
schema:
type: object
examples:
example-0:
summary: error (prime number too big)
value:
error: the number you want to check has to be < 10^12
example-1:
summary: error (alpha number)
value:
error: the number you want to check has to be an integer
example-2:
summary: error (no number)
value:
error: please include the number you want to check
undefined:
content:
text/plain:
schema:
type: string
example: ''
/get-all-primes-between-two-numbers.php:
get:
tags:
- General
summary: get-all-primes-between-two-numbers (paid)
parameters:
- name: key
in: query
schema:
type: string
description: (Required) your API key
example: '{{apiKey}}'
- name: include_explanations
in: query
schema:
type: string
description: >-
includes the full explanations for each item if true (default is
false)
example:
- name: include_prime_types_list
in: query
schema:
type: string
description: >-
includes the full prime types list for each item if true (default is
false)
example:
- name: language
in: query
schema:
type: string
description: >-
show the output translated into that language (it can be english,
mandarin, hindi, spanish, french, german, italian, japanese,
russian) (default is english)
example:
responses:
'200':
description: OK
headers:
Date:
schema:
type: string
example: Tue, 21 Sep 2021 22:41:43 GMT
Server:
schema:
type: string
example: Apache
Access-Control-Allow-Origin:
schema:
type: string
example: '*'
Keep-Alive:
schema:
type: string
example: timeout=5, max=100
Connection:
schema:
type: string
example: Keep-Alive
Transfer-Encoding:
schema:
type: string
example: chunked
Content-Type:
schema:
type: string
example: application/json
content:
application/json:
schema:
type: object
examples:
example-0:
summary: success (with start / stop numbers)
value:
- random_prime_number_value: 353
base_conversions:
binary_value: '101100001'
senary_value: '1345'
hexa_value: '161'
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 19
computations in 0.00078284559283566 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 359
base_conversions:
binary_value: '101100111'
senary_value: '1355'
hexa_value: '167'
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 19
computations in 0.00078947063839568 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 361
base_conversions:
binary_value: '101101001'
senary_value: '1401'
hexa_value: '169'
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-09-02 00:24:57: server mac-server processed 19
computations in 0.00079166666666667 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 367
base_conversions:
binary_value: '101101111'
senary_value: '1411'
hexa_value: 16f
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 19
computations in 0.00079821850252783 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 373
base_conversions:
binary_value: '101110101'
senary_value: '1421'
hexa_value: '175'
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 19
computations in 0.00080471699649283 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 379
base_conversions:
binary_value: '101111011'
senary_value: '1431'
hexa_value: 17b
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 19
computations in 0.00081116343058049 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 383
base_conversions:
binary_value: '101111111'
senary_value: '1435'
hexa_value: 17f
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 20
computations in 0.00081543274128254 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 389
base_conversions:
binary_value: '110000101'
senary_value: '1445'
hexa_value: '185'
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 20
computations in 0.00082179512180483 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 397
base_conversions:
binary_value: '110001101'
senary_value: '1501'
hexa_value: 18d
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 20
computations in 0.00083020245188214 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 401
base_conversions:
binary_value: '110010001'
senary_value: '1505'
hexa_value: '191'
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 20
computations in 0.00083437434977087 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 409
base_conversions:
binary_value: '110011001'
senary_value: '1521'
hexa_value: '199'
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 20
computations in 0.00084265618400653 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 419
base_conversions:
binary_value: '110100011'
senary_value: '1535'
hexa_value: 1a3
previous_prime_gap: 10
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 20
computations in 0.00085289539543578 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 421
base_conversions:
binary_value: '110100101'
senary_value: '1541'
hexa_value: 1a5
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 21
computations in 0.00085492852202847 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 431
base_conversions:
binary_value: '110101111'
senary_value: '1555'
hexa_value: 1af
previous_prime_gap: 10
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 21
computations in 0.00086502247883445 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 433
base_conversions:
binary_value: '110110001'
senary_value: '2001'
hexa_value: 1b1
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 21
computations in 0.00086702716861187 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 439
base_conversions:
binary_value: '110110111'
senary_value: '2011'
hexa_value: 1b7
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 21
computations in 0.00087301361832321 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 443
base_conversions:
binary_value: '110111011'
senary_value: '2015'
hexa_value: 1bb
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 21
computations in 0.00087698188249372 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 449
base_conversions:
binary_value: '111000001'
senary_value: '2025'
hexa_value: 1c1
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 21
computations in 0.00088290083751738 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 457
base_conversions:
binary_value: '111001001'
senary_value: '2041'
hexa_value: 1c9
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 21
computations in 0.00089073159693466 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 461
base_conversions:
binary_value: '111001101'
senary_value: '2045'
hexa_value: 1cd
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 21
computations in 0.000894621273066 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 463
base_conversions:
binary_value: '111001111'
senary_value: '2051'
hexa_value: 1cf
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 22
computations in 0.00089655978297292 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 467
base_conversions:
binary_value: '111010011'
senary_value: '2055'
hexa_value: 1d3
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 22
computations in 0.00090042428270726 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 479
base_conversions:
binary_value: '111011111'
senary_value: '2115'
hexa_value: 1df
previous_prime_gap: 12
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 22
computations in 0.00091191952617664 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 487
base_conversions:
binary_value: '111100111'
senary_value: '2131'
hexa_value: '1e7'
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 22
computations in 0.00091950318711308 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 491
base_conversions:
binary_value: '111101011'
senary_value: '2135'
hexa_value: 1eb
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 22
computations in 0.00092327165859001 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 499
base_conversions:
binary_value: '111110011'
senary_value: '2151'
hexa_value: 1f3
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 22
computations in 0.00093076282932036 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 503
base_conversions:
binary_value: '111110111'
senary_value: '2155'
hexa_value: 1f7
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 22
computations in 0.00093448589550024 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 509
base_conversions:
binary_value: '111111101'
senary_value: '2205'
hexa_value: 1fd
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 23
computations in 0.00094004284772321 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 521
base_conversions:
binary_value: '1000001001'
senary_value: '2225'
hexa_value: '209'
previous_prime_gap: 12
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 23
computations in 0.00095105935087611 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 523
base_conversions:
binary_value: '1000001011'
senary_value: '2231'
hexa_value: 20b
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 23
computations in 0.00095288305216911 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 529
base_conversions:
binary_value: '1000010001'
senary_value: '2241'
hexa_value: '211'
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-09-02 00:24:57: server mac-server processed 23
computations in 0.00095833333333333 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 541
base_conversions:
binary_value: '1000011101'
senary_value: '2301'
hexa_value: 21d
previous_prime_gap: 12
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 23
computations in 0.00096914194580108 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 547
base_conversions:
binary_value: '1000100011'
senary_value: '2311'
hexa_value: '223'
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 23
computations in 0.00097450129696054 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 557
base_conversions:
binary_value: '1000101101'
senary_value: '2325'
hexa_value: 22d
previous_prime_gap: 10
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 24
computations in 0.00098336864343383 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 563
base_conversions:
binary_value: '1000110011'
senary_value: '2335'
hexa_value: '233'
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 24
computations in 0.00098865087647539 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 569
base_conversions:
binary_value: '1000111001'
senary_value: '2345'
hexa_value: '239'
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 24
computations in 0.00099390503682305 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 571
base_conversions:
binary_value: '1000111011'
senary_value: '2351'
hexa_value: 23b
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 24
computations in 0.00099565026211238 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 577
base_conversions:
binary_value: '1001000001'
senary_value: '2401'
hexa_value: '241'
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 24
computations in 0.001000867679122 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 587
base_conversions:
binary_value: '1001001011'
senary_value: '2415'
hexa_value: 24b
previous_prime_gap: 10
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 24
computations in 0.0010095034532988 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 593
base_conversions:
binary_value: '1001010001'
senary_value: '2425'
hexa_value: '251'
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 24
computations in 0.0010146496384905 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 599
base_conversions:
binary_value: '1001010111'
senary_value: '2435'
hexa_value: '257'
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 24
computations in 0.00101976985421 micro-seconds using 2 x
3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 601
base_conversions:
binary_value: '1001011001'
senary_value: '2441'
hexa_value: '259'
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 25
computations in 0.0010214708893443 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 607
base_conversions:
binary_value: '1001011111'
senary_value: '2451'
hexa_value: 25f
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 25
computations in 0.0010265570828962 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 613
base_conversions:
binary_value: '1001100101'
senary_value: '2501'
hexa_value: '265'
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 25
computations in 0.0010316182002617 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 617
base_conversions:
binary_value: '1001101001'
senary_value: '2505'
hexa_value: '269'
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 25
computations in 0.0010349785290312 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 619
base_conversions:
binary_value: '1001101011'
senary_value: '2511'
hexa_value: 26b
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 25
computations in 0.0010366546087187 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 631
base_conversions:
binary_value: '1001110111'
senary_value: '2531'
hexa_value: '277'
previous_prime_gap: 12
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 25
computations in 0.0010466547239234 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 641
base_conversions:
binary_value: '1010000001'
senary_value: '2545'
hexa_value: '281'
previous_prime_gap: 10
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 25
computations in 0.0010549157417643 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 643
base_conversions:
binary_value: '1010000011'
senary_value: '2551'
hexa_value: '283'
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 25
computations in 0.0010565601944255 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 647
base_conversions:
binary_value: '1010000111'
senary_value: '2555'
hexa_value: '287'
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 25
computations in 0.0010598414451647 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 653
base_conversions:
binary_value: '1010001101'
senary_value: '3005'
hexa_value: 28d
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 26
computations in 0.0010647443615984 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 659
base_conversions:
binary_value: '1010010011'
senary_value: '3015'
hexa_value: '293'
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 26
computations in 0.0010696248044161 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 661
base_conversions:
binary_value: '1010010101'
senary_value: '3021'
hexa_value: '295'
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 26
computations in 0.0010712466776819 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 673
base_conversions:
binary_value: '1010100001'
senary_value: '3041'
hexa_value: 2a1
previous_prime_gap: 12
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 26
computations in 0.0010809268142561 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 677
base_conversions:
binary_value: '1010100101'
senary_value: '3045'
hexa_value: 2a5
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 26
computations in 0.0010841343192715 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 683
base_conversions:
binary_value: '1010101011'
senary_value: '3055'
hexa_value: 2ab
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 26
computations in 0.0010889278621143 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 691
base_conversions:
binary_value: '1010110011'
senary_value: '3111'
hexa_value: 2b3
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 26
computations in 0.0010952866190079 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 701
base_conversions:
binary_value: '1010111101'
senary_value: '3125'
hexa_value: 2bd
previous_prime_gap: 10
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 26
computations in 0.0011031835245728 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 709
base_conversions:
binary_value: '1011000101'
senary_value: '3141'
hexa_value: 2c5
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 27
computations in 0.0011094605796412 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 719
base_conversions:
binary_value: '1011001111'
senary_value: '3155'
hexa_value: 2cf
previous_prime_gap: 10
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 27
computations in 0.0011172573064827 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 727
base_conversions:
binary_value: '1011010111'
senary_value: '3211'
hexa_value: 2d7
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 27
computations in 0.0011234557302261 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 733
base_conversions:
binary_value: '1011011101'
senary_value: '3221'
hexa_value: 2dd
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 27
computations in 0.0011280821975567 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 739
base_conversions:
binary_value: '1011100011'
senary_value: '3231'
hexa_value: '2e3'
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 27
computations in 0.0011326897682557 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 743
base_conversions:
binary_value: '1011100111'
senary_value: '3235'
hexa_value: '2e7'
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 27
computations in 0.0011357510975366 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 751
base_conversions:
binary_value: '1011101111'
senary_value: '3251'
hexa_value: 2ef
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 27
computations in 0.0011418491338371 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 757
base_conversions:
binary_value: '1011110101'
senary_value: '3301'
hexa_value: 2f5
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 28
computations in 0.0011464013743498 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 761
base_conversions:
binary_value: '1011111001'
senary_value: '3305'
hexa_value: 2f9
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 28
computations in 0.0011494261853445 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 769
base_conversions:
binary_value: '1100000001'
senary_value: '3321'
hexa_value: '301'
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 28
computations in 0.0011554520519885 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 773
base_conversions:
binary_value: '1100000101'
senary_value: '3325'
hexa_value: '305'
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 28
computations in 0.0011584532312048 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 787
base_conversions:
binary_value: '1100010011'
senary_value: '3351'
hexa_value: '313'
previous_prime_gap: 14
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 28
computations in 0.0011688966782588 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 797
base_conversions:
binary_value: '1100011101'
senary_value: '3405'
hexa_value: 31d
previous_prime_gap: 10
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 28
computations in 0.0011762995177911 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 809
base_conversions:
binary_value: '1100101001'
senary_value: '3425'
hexa_value: '329'
previous_prime_gap: 12
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 28
computations in 0.0011851218877773 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 811
base_conversions:
binary_value: '1100101011'
senary_value: '3431'
hexa_value: 32b
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 28
computations in 0.0011865859054915 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 821
base_conversions:
binary_value: '1100110101'
senary_value: '3445'
hexa_value: '335'
previous_prime_gap: 10
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 29
computations in 0.0011938790651579 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 823
base_conversions:
binary_value: '1100110111'
senary_value: '3451'
hexa_value: '337'
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 29
computations in 0.0011953323573151 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 827
base_conversions:
binary_value: '1100111011'
senary_value: '3455'
hexa_value: 33b
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 29
computations in 0.0011982336537124 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 829
base_conversions:
binary_value: '1100111101'
senary_value: '3501'
hexa_value: 33d
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 29
computations in 0.0011996816707407 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 839
base_conversions:
binary_value: '1101000111'
senary_value: '3515'
hexa_value: '347'
previous_prime_gap: 10
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 29
computations in 0.0012068956964967 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 841
base_conversions:
binary_value: '1101001001'
senary_value: '3521'
hexa_value: '349'
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-09-02 00:24:58: server mac-server processed 29
computations in 0.0012083333333333 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 853
base_conversions:
binary_value: '1101010101'
senary_value: '3541'
hexa_value: '355'
previous_prime_gap: 12
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 29
computations in 0.0012169234888759 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 857
base_conversions:
binary_value: '1101011001'
senary_value: '3545'
hexa_value: '359'
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 29
computations in 0.001219773430692 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 859
base_conversions:
binary_value: '1101011011'
senary_value: '3551'
hexa_value: 35b
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 29
computations in 0.0012211959074794 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 863
base_conversions:
binary_value: '1101011111'
senary_value: '3555'
hexa_value: 35f
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 29
computations in 0.0012240359017974 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 877
base_conversions:
binary_value: '1101101101'
senary_value: '4021'
hexa_value: 36d
previous_prime_gap: 14
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 30
computations in 0.0012339244079134 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 881
base_conversions:
binary_value: '1101110001'
senary_value: '4025'
hexa_value: '371'
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 30
computations in 0.0012367351733047 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 883
base_conversions:
binary_value: '1101110011'
senary_value: '4031'
hexa_value: '373'
previous_prime_gap: 2
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 30
computations in 0.0012381381631753 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 887
base_conversions:
binary_value: '1101110111'
senary_value: '4035'
hexa_value: '377'
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 30
computations in 0.0012409393843196 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 899
base_conversions:
binary_value: '1110000011'
senary_value: '4055'
hexa_value: '383'
previous_prime_gap: 12
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-09-02 00:24:58: server mac-server processed 30
computations in 0.0012493053625471 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 907
base_conversions:
binary_value: '1110001011'
senary_value: '4111'
hexa_value: 38b
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 30
computations in 0.0012548516955313 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 911
base_conversions:
binary_value: '1110001111'
senary_value: '4115'
hexa_value: 38f
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 30
computations in 0.0012576156893989 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 919
base_conversions:
binary_value: '1110010111'
senary_value: '4131'
hexa_value: '397'
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 30
computations in 0.001263125532602 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 929
base_conversions:
binary_value: '1110100001'
senary_value: '4145'
hexa_value: 3a1
previous_prime_gap: 10
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 30
computations in 0.0012699792211773 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 937
base_conversions:
binary_value: '1110101001'
senary_value: '4201'
hexa_value: 3a9
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 31
computations in 0.0012754356554178 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 941
base_conversions:
binary_value: '1110101101'
senary_value: '4205'
hexa_value: 3ad
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 31
computations in 0.0012781551375148 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 947
base_conversions:
binary_value: '1110110011'
senary_value: '4215'
hexa_value: 3b3
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 31
computations in 0.0012822235461191 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 953
base_conversions:
binary_value: '1110111001'
senary_value: '4225'
hexa_value: 3b9
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 31
computations in 0.0012862790867028 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 961
base_conversions:
binary_value: '1111000001'
senary_value: '4241'
hexa_value: 3c1
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-09-02 00:24:58: server mac-server processed 31
computations in 0.0012916666666667 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 967
base_conversions:
binary_value: '1111000111'
senary_value: '4251'
hexa_value: 3c7
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 31
computations in 0.0012956926504555 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 971
base_conversions:
binary_value: '1111001011'
senary_value: '4255'
hexa_value: 3cb
previous_prime_gap: 4
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 31
computations in 0.0012983697042402 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 977
base_conversions:
binary_value: '1111010001'
senary_value: '4305'
hexa_value: 3d1
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 31
computations in 0.0013023749673406 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 983
base_conversions:
binary_value: '1111010111'
senary_value: '4315'
hexa_value: 3d7
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 31
computations in 0.0013063679505492 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 991
base_conversions:
binary_value: '1111011111'
senary_value: '4331'
hexa_value: 3df
previous_prime_gap: 8
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 31
computations in 0.0013116730198914 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
- random_prime_number_value: 997
base_conversions:
binary_value: '1111100101'
senary_value: '4341'
hexa_value: '3e5'
previous_prime_gap: 6
prime_density: '7.86960000'
isolated_primes:
is_isolated_prime: 'false'
isolated_prime_density: '7.86960000'
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 32
computations in 0.0013156377836539 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
example-1:
summary: >-
success (with start / stop numbers, explanations and
prime_types)
value:
- random_prime_number_value: 71
base_conversions:
binary_value: '1000111'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '155'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: '47'
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 4
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 73
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 67
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'true'
reversible_emirp_value: 17
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 8
computations in 0.00035108957388235 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 73
base_conversions:
binary_value: '1001001'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '201'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: '49'
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 2
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 71
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'false'
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 79
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'true'
reversible_emirp_value: 37
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 9
computations in 0.0003560001560549 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 79
base_conversions:
binary_value: '1001111'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '211'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: 4f
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 6
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'false'
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 83
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 73
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'true'
reversible_emirp_value: 97
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 9
computations in 0.00037034143405482 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 83
base_conversions:
binary_value: '1010011'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '215'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: '53'
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 4
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'false'
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 79
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 89
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 9
computations in 0.00037960139913101 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 89
base_conversions:
binary_value: '1011001'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '225'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: '59'
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 6
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'false'
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'false'
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 83
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'true'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 9
computations in 0.00039308254716903 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 97
base_conversions:
binary_value: '1100001'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '241'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: '61'
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 8
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'false'
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 101
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'true'
reversible_emirp_value: 79
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 10
computations in 0.00041036907507484 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 101
base_conversions:
binary_value: '1100101'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '245'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: '65'
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 4
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'true'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 103
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 97
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 10
computations in 0.0004187448175467 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 103
base_conversions:
binary_value: '1100111'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '251'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: '67'
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 2
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 101
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 107
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 10
computations in 0.00042287048187884 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 107
base_conversions:
binary_value: '1101011'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '255'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: 6b
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 4
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 109
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 103
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'true'
reversible_emirp_value: 701
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 10
computations in 0.00043100335136619 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 109
base_conversions:
binary_value: '1101101'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '301'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: 6d
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 2
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 107
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 113
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 10
computations in 0.00043501277120461 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 113
base_conversions:
binary_value: '1110001'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '305'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: '71'
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 4
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'false'
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 109
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'true'
reversible_emirp_value: 311
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 11
computations in 0.00044292274219728 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 121
base_conversions:
binary_value: '1111001'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '321'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: '79'
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 8
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'true'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'false'
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'false'
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 127
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-09-02 00:24:57: server mac-server processed 11
computations in 0.00045833333333333 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 127
base_conversions:
binary_value: '1111111'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '331'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: 7f
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 6
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'false'
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 131
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 121
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'true'
power_of_two_value: 7
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 11
computations in 0.00046955948623269 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 131
base_conversions:
binary_value: '10000011'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '335'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: '83'
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 4
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'true'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'false'
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 127
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 137
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 11
computations in 0.00047689679759415 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 137
base_conversions:
binary_value: '10001001'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '345'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: '89'
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 6
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 139
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'false'
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 131
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 12
computations in 0.00048769582961332 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 139
base_conversions:
binary_value: '10001011'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '351'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: 8b
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 2
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 137
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 143
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 12
computations in 0.00049124275510632 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 143
base_conversions:
binary_value: '10001111'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '355'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: 8f
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 4
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'false'
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 139
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 149
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-09-02 00:24:57: server mac-server processed 12
computations in 0.00049826086429589 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 149
base_conversions:
binary_value: '10010101'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '405'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: '95'
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 6
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 151
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'false'
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 143
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'true'
reversible_emirp_value: 941
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 12
computations in 0.0005086064839889 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 151
base_conversions:
binary_value: '10010111'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '411'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: '97'
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 2
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'true'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 149
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'false'
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 157
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 12
computations in 0.00051200857197685 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 157
base_conversions:
binary_value: '10011101'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '421'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: 9d
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 6
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'false'
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'false'
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 163
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'true'
reversible_emirp_value: 751
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 13
computations in 0.00052208183692257 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 163
base_conversions:
binary_value: '10100011'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '431'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: a3
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 6
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'false'
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 167
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 157
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 13
computations in 0.00053196438895015 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 167
base_conversions:
binary_value: '10100111'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '435'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: a7
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 4
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 169
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 163
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'true'
reversible_emirp_value: 761
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 13
computations in 0.000538451999305 micro-seconds using 2
x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 169
base_conversions:
binary_value: '10101001'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '441'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: a9
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 2
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 167
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 173
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-09-02 00:24:57: server mac-server processed 13
computations in 0.00054166666666667 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 173
base_conversions:
binary_value: '10101101'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '445'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: ad
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 4
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'false'
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 169
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 179
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 13
computations in 0.00054803943491525 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 179
base_conversions:
binary_value: '10110011'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '455'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: b3
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 6
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 181
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'false'
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'true'
sexy_value: 173
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'true'
reversible_emirp_value: 971
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 13
computations in 0.00055746200667749 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 181
base_conversions:
binary_value: '10110101'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '501'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: b5
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 2
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'true'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 179
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'false'
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 13
computations in 0.00056056766862807 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 191
base_conversions:
binary_value: '10111111'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '515'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: bf
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 10
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'true'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 193
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'false'
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 14
computations in 0.00057584479004522 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 193
base_conversions:
binary_value: '11000001'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '521'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: c1
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 2
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 191
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 197
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 14
computations in 0.00057885183289374 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 197
base_conversions:
binary_value: '11000101'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '525'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: c5
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 4
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 199
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'true'
cousin_value: 193
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 14
computations in 0.00058481953531742 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
- random_prime_number_value: 199
base_conversions:
binary_value: '11000111'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '531'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: c7
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 2
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '7.86960000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 0 and 1 000 000)
isolated_primes:
is_isolated_prime: 'false'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
isolated_prime_density: '7.86960000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated
prime number in this million composite numbers
(between 0 and 1 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples:
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353,
373, 383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.01190000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_twin: 'true'
twin_value: 197
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '1.64450000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_cousin: 'false'
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '1.63800000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17),
(13,19), (17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '2.52870000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 0 and 1 000 000)
is_reversible: 'true'
reversible_emirp_value: 991
reversible_explanation: >-
primes that become a different prime when their
decimal digits are reversed. The name emirp is
obtained by reversing the word prime (examples: 13,
17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157)
(reference: https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '1.12150000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance
of each base digit. (examples: 2143 (base 4), 7654321
(base 7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00210000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00010000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form
2n - 1 (one less than a power of two) for some integer
n. They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00080000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers
(examples: 2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00090000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 0 and 1 000
000)
birth_certificate: >-
2018-06-16 22:01:25: server mac-server processed 14
computations in 0.00058778066581941 micro-seconds using
2 x 3 GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
'403':
description: Forbidden
headers:
Date:
schema:
type: string
example: Sat, 11 Sep 2021 23:16:49 GMT
Server:
schema:
type: string
example: Apache
Access-Control-Allow-Origin:
schema:
type: string
example: '*'
X-PHP-Response-Code:
schema:
type: integer
example: '403'
Keep-Alive:
schema:
type: string
example: timeout=5, max=100
Connection:
schema:
type: string
example: Keep-Alive
Transfer-Encoding:
schema:
type: string
example: chunked
Content-Type:
schema:
type: string
example: application/json
content:
application/json:
schema:
type: object
example:
error: please include the api key in your query
'404':
description: Not Found
headers:
Date:
schema:
type: string
example: Sat, 11 Sep 2021 23:18:46 GMT
Server:
schema:
type: string
example: Apache
Access-Control-Allow-Origin:
schema:
type: string
example: '*'
X-PHP-Response-Code:
schema:
type: integer
example: '404'
Keep-Alive:
schema:
type: string
example: timeout=5, max=100
Connection:
schema:
type: string
example: Keep-Alive
Transfer-Encoding:
schema:
type: string
example: chunked
Content-Type:
schema:
type: string
example: application/json
content:
application/json:
schema:
type: object
examples:
example-0:
summary: error (alpha end number)
value:
error: please include end number < 122 302 891 547
example-1:
summary: error (no start number)
value:
error: >-
start number not specified; start number has to be an
integer > 2
example-2:
summary: error (start number too small)
value:
error: minimum allowed start number has to be > 2
example-3:
summary: error (end number smaller than the start number)
value:
error: start number has to be < end number
example-4:
summary: error (alpha start number)
value:
error: start number has to be an integer > 2
example-5:
summary: error (no results)
value:
error: no numbers found
example-6:
summary: error (start number more than maximum)
value:
error: start number has to be < end number
example-7:
summary: error (no end number)
value:
error: >-
end number not specified; please include end number has to
be an integer < 122 302 837 649
example-8:
summary: error (end number more than maximum)
value:
error: maximum allowed end number has to be < 122 302 958 123
/prospect-primes-between-two-numbers.php:
get:
tags:
- General
summary: prospect-primes-between-two-numbers (paid)
parameters:
- name: key
in: query
schema:
type: string
description: (Required) your API key
example: '{{apiKey}}'
- name: include_explanations
in: query
schema:
type: string
description: >-
includes the full explanations for each item if true (default is
false)
example:
- name: include_prime_types_list
in: query
schema:
type: string
description: >-
includes the full prime types list for each item if true (default is
false)
example:
- name: start
in: query
schema:
type: string
description: >-
(Required if the end is specified) the number from which the process
will start (needs to be smaller than the end)
example:
- name: end
in: query
schema:
type: string
description: >-
(Required if the start is specified) the number to which the process
will end (needs to be larger than the start)
example:
- name: language
in: query
schema:
type: string
description: >-
show the output translated into that language (it can be english,
mandarin, hindi, spanish, french, german, italian, japanese,
russian) (default is english)
example:
responses:
'200':
description: OK
headers:
Date:
schema:
type: string
example: Tue, 21 Sep 2021 23:13:45 GMT
Server:
schema:
type: string
example: Apache
Access-Control-Allow-Origin:
schema:
type: string
example: '*'
Keep-Alive:
schema:
type: string
example: timeout=5, max=100
Connection:
schema:
type: string
example: Keep-Alive
Transfer-Encoding:
schema:
type: string
example: chunked
Content-Type:
schema:
type: string
example: application/json
content:
application/json:
schema:
type: object
example:
query_info:
user_start_input: 99999
user_end_input: 999999999
calculated_initial_density_value: 0
calculated_initial_density_value_explanation: start number (99999) rounded down to the previous million
calculated_final_density_value: 1000000000
calculated_final_density_value_explanation: end number (999999999) rounded up to the next million
average_densities:
all_primes: '5.085141700000'
all_primes_explanation: >-
average primes density numbers (%) (between 0 and 1 000 000
000)
isolated_primes: '0.000010200000'
isolated_primes_explanation: >-
average isolated primes density numbers (%) (between 0 and 1
000 000 000) [ isolated primes details ==> prime numbers
that are more than 100 composite numbers away from each of
their neighbours, with an average density of 0.000124565509%
]
palindrome_density: '0.000595900000'
palindrome_density_explanation: >-
average palindrome primes density numbers (%) between 0 and
1 000 000 000); [ palindrome prime number details ==> number
that is simultaneously palindromic (which reads the same
backwards as forwards) and prime (examples: 2, 3, 5, 7, 11,
101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787,
797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime) ]
twin_density: '0.685039900000'
twin_density_explanation: >-
average twin primes density numbers (%) between 0 and 1 000
000 000); [ twin prime number details ==> primes that are no
more than 2 composite numbers from each other (examples: (3,
5), (5, 7), (11, 13), (17, 19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime) ]
cousin_density: '0.685034600000'
cousin_density_explanation: >-
average cousin primes density numbers (%) between 0 and 1
000 000 000); [ cousin prime number details ==> primes that
are no more than 4 composite numbers from each other
(examples: (3, 7), (7, 11), (13, 17), (19, 23), (37, 41),
(43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime) ]
sexy_density: '1.158574100000'
sexy_density_explanation: >-
average sexy primes density numbers (%) between 0 and 1 000
000 000); [ sexy prime number details ==> primes that are no
more than 6 composite numbers from each other (examples:
(5,11), (7,13), (11,17), (13,19), (17,23), (23,29))
(reference: https://en.wikipedia.org/wiki/Sexy_prime) ]
reversible_density: '0.480967000000'
reversible_density_explanation: >-
average reversible primes density numbers (%) between 0 and
1 000 000 000); [ reversible prime number details ==> primes
that become a different prime when their decimal digits are
reversed. The name emirp is obtained by reversing the word
prime (examples: 13, 17, 31, 37, 71, 73, 79, 97, 107, 113,
149, 157) (reference: https://en.wikipedia.org/wiki/Emirp) ]
pandigital_density: '0.000322300000'
pandigital_density_explanation: >-
average pandigital primes density numbers (%) between 0 and
1 000 000 000); [ pandigital prime number details ==>
pandigital prime in a base has at least one instance of each
base digit. (examples: 2143 (base 4), 7654321 (base 7))
(reference:
https://www.xarg.org/puzzle/project-euler/problem-41/) ]
repunit_density: '0.000000100000'
repunit_density_explanation: >-
average repunit primes density numbers (%) between 0 and 1
000 000 000); [ repunit prime number details ==> repunits
primes are positive integers in which every digit is one
(examples: 11, 1111111111111111111) (reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit) ]
mersenne_density: '0.000000800000'
mersenne_density_explanation: >-
average mersenne primes density numbers (%) between 0 and 1
000 000 000); [ mersenne prime number details ==> mersenne
prime is a prime number that is of the form 2n - 1 (one less
than a power of two) for some integer n. They are named
after Marin Mersenne (1588-1648), a French monk who studied
them in his Cogitata Physica-Mathematica (1644) (examples: 3
(2^2 - 1), 7 (2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/) ]
fibonacci_density: '0.000001000000'
fibonacci_density_explanation: >-
average fibonacci primes density numbers (%) between 0 and 1
000 000 000); [ fibonacci prime number details ==> prime
numbers that are also Fibonacci numbers (examples: 2, 3, 5,
13, 89, 233, 1597) (reference: https://oeis.org/A005478) ]
'403':
description: Forbidden
headers:
Date:
schema:
type: string
example: Sat, 11 Sep 2021 23:21:37 GMT
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schema:
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example:
error: please include the api key in your query
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headers:
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example: Sat, 11 Sep 2021 23:30:43 GMT
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schema:
type: string
example: application/json
content:
application/json:
schema:
type: object
examples:
example-0:
summary: error (no end number)
value:
error: >-
end number not specified; please include end number has to
be an integer < 122 304 000 000
example-1:
summary: error (end number more than maximum)
value:
error: maximum allowed end number has to be < 122 302 000 000
example-2:
summary: error (start number too small)
value:
error: minimum allowed start number has to be > 2
example-3:
summary: error (end number smaller than the start number)
value:
error: start number has to be < end number
example-4:
summary: error (alpha start number)
value:
error: start number has to be an integer > 2
example-5:
summary: error (no start number)
value:
error: >-
start number not specified; please include start number
has to be an integer > 2
example-6:
summary: error (start number more than maximum)
value:
error: maximum allowed start number has to be < 122 302 000 000
example-7:
summary: error (alpha end number)
value:
error: >-
please include end number has to be an integer < 122 302
000 000
undefined:
content:
text/plain:
schema:
type: string
example: ''
/get-isolated-random-prime.php:
get:
tags:
- General
summary: get-isolated-random-prime (paid)
parameters:
- name: key
in: query
schema:
type: string
description: (Required) your API key
example: '{{apiKey}}'
- name: include_explanations
in: query
schema:
type: string
description: >-
includes the full explanations for each item if true (default is
false)
example:
- name: include_prime_types_list
in: query
schema:
type: string
description: >-
includes the full prime types list for each item if true (default is
false)
example:
- name: minimum_combined_prime_gap
in: query
schema:
type: string
description: >-
the total numbers of neighbouring composite numbers on the right and
on the left of the current prime number, determines how isolated
this prime is and how hard it is to find it (value between 200 and
500) (default is 200)
example:
- name: language
in: query
schema:
type: string
description: >-
show the output translated into that language (it can be english,
mandarin, hindi, spanish, french, german, italian, japanese,
russian) (default is english)
example:
responses:
'200':
description: OK
headers:
Date:
schema:
type: string
example: Tue, 21 Sep 2021 22:45:59 GMT
Server:
schema:
type: string
example: Apache
Access-Control-Allow-Origin:
schema:
type: string
example: '*'
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schema:
type: string
example: timeout=5, max=100
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schema:
type: string
example: Keep-Alive
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schema:
type: string
example: chunked
Content-Type:
schema:
type: string
example: application/json
content:
application/json:
schema:
type: object
examples:
example-0:
summary: >-
success (with explanations, prime_types and
minimum_combined_prime_gap)
value:
random_prime_number_value: 31587561361
minimum_combined_prime_gap_value: 500
minimum_combined_prime_gap_value_explanation: >-
Minimum gap on on both sides of this isolated prime number
(the higher the value the less chances for that number for
that prime number to be randomly found)
base_conversions:
binary_value: '11101011010110000111110111110010001'
binary_value_explanation: >-
prime number base-2 (binary value), useful for
cryptography and cryptocurrency
senary_value: '22302223022001'
senary_value_explanation: >-
prime number base-6 (senary value), useful for
mathematical research
hexa_value: 75ac3ef91
hexa_value_explanation: >-
prime number base-16 (hexa value), useful for
cryptography and cryptocurrency
previous_prime_gap: 222
previous_prime_gap_explanation: >-
how many successive prime and composite numbers are
between this prime and the previous one
prime_density: '4.14510000'
prime_density_explanation: >-
how many prime numbers (%) can be found in this million
composite numbers (between 31 587 000 000 and 31 588 000
000)
isolated_primes:
is_isolated_prime: 'true'
is_isolated_prime_explanation: >-
prime numbers that are more than 100 composite numbers
away from each of their neighbours, with an average
density of 0.000124565509%
combined_gap: 502
previous_prime_gap: 222
next_prime_gap: 280
isolated_prime_density: '4.14510000'
isolated_prime_density_explanation: >-
how many chances (%) to randomly find an isolated prime
number in this million composite numbers (between 31 587
000 000 and 31 588 000 000)
prime_types:
is_palindrome: 'false'
palindrome_explanation: >-
number that is simultaneously palindromic (which reads
the same backwards as forwards) and prime (examples: 2,
3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373,
383, 727, 757, 787, 797, 919, 929) (reference:
https://en.wikipedia.org/wiki/Palindromic_prime)
palindrome_percentage: '0.00010000'
palindrome_density_explanation: >-
how many palindrome prime numbers (%) can be found in
this million composite numbers (between 31 587 000 000
and 31 588 000 000)
is_twin: 'false'
twin_explanation: >-
primes that are no more than 2 composite numbers from
each other (examples: (3, 5), (5, 7), (11, 13), (17,
19)) (reference:
https://en.wikipedia.org/wiki/Twin_prime)
twin_percentage: '0.46460000'
twin_density_explanation: >-
how many twin prime numbers (%) can be found in this
million composite numbers (between 31 587 000 000 and 31
588 000 000)
is_cousin: 'false'
cousin_explanation: >-
primes that are no more than 4 composite numbers from
each other (examples: (3, 7), (7, 11), (13, 17), (19,
23), (37, 41), (43, 47)) (reference:
https://en.wikipedia.org/wiki/Cousin_prime)
cousin_percentage: '0.44980000'
cousin_density_explanation: >-
how many cousin prime numbers (%) can be found in this
million composite numbers (between 31 587 000 000 and 31
588 000 000)
is_sexy: 'false'
sexy_explanation: >-
primes that are no more than 6 composite numbers from
each other (examples: (5,11), (7,13), (11,17), (13,19),
(17,23), (23,29)) (reference:
https://en.wikipedia.org/wiki/Sexy_prime)
sexy_percentage: '0.80110000'
sexy_density_explanation: >-
how many sexy prime numbers (%) can be found in this
million composite numbers (between 31 587 000 000 and 31
588 000 000)
is_reversible: 'false'
reversible_explanation: >-
primes that become a different prime when their decimal
digits are reversed. The name emirp is obtained by
reversing the word prime (examples: 13, 17, 31, 37, 71,
73, 79, 97, 107, 113, 149, 157) (reference:
https://en.wikipedia.org/wiki/Emirp)
reversible_percentage: '0.69950000'
reversible_density_explanation: >-
how many reversible prime numbers (%) can be found in
this million composite numbers (between 31 587 000 000
and 31 588 000 000)
is_pandigital: 'false'
pandigital_explanation: >-
pandigital prime in a base has at least one instance of
each base digit. (examples: 2143 (base 4), 7654321 (base
7)) (reference:
https://www.xarg.org/puzzle/project-euler/problem-41/)
pandigital_percentage: '0.00000000'
pandigital_density_explanation: >-
how many pandigital prime numbers (%) can be found in
this million composite numbers (between 31 587 000 000
and 31 588 000 000)
is_repunit: 'false'
repunit_explanation: >-
repunits primes are positive integers in which every
digit is one (examples: 11, 1111111111111111111)
(reference:
https://primes.utm.edu/glossary/page.php?sort=Repunit)
repunit_percentage: '0.00000000'
repunit_density_explanation: >-
how many repunit prime numbers (%) can be found in this
million composite numbers (between 31 587 000 000 and 31
588 000 000)
is_mersenne: 'false'
mersenne_explanation: >-
mersenne prime is a prime number that is of the form 2n
- 1 (one less than a power of two) for some integer n.
They are named after Marin Mersenne (1588-1648), a
French monk who studied them in his Cogitata
Physica-Mathematica (1644) (examples: 3 (2^2 - 1), 7
(2^3 - 1), 31 (2^5 - 1) ) (reference:
https://www.mersenne.org/)
mersenne_percentage: '0.00000000'
mersenne_density_explanation: >-
how many mersenne prime numbers (%) can be found in this
million composite numbers (between 31 587 000 000 and 31
588 000 000)
is_fibonacci: 'false'
fibonacci_explanation: >-
prime numbers that are also Fibonacci numbers (examples:
2, 3, 5, 13, 89, 233, 1597) (reference:
https://oeis.org/A005478)
fibonacci_percentage: '0.00000000'
fibonacci_density_explanation: >-
how many fibonacci prime numbers (%) can be found in
this million composite numbers (between 31 587 000 000
and 31 588 000 000)
birth_certificate: >-
2019-06-14 19:36:06: server mac-server processed 177 729
computations in 7.4053707707134 micro-seconds using 2 x 3
GHz Quad-Core Intel Xeon CPUs
birth_certificate_explanation: >-
how many computations, how much time and what computer
power was used to find this prime number
example-1:
summary: success (no query params)
value:
random_prime_number_value: 32341799407
minimum_combined_prime_gap_value: 200
base_conversions:
binary_value: '11110000111101110001011000111101111'
senary_value: '22505125000451'
hexa_value: 787b8b1ef
previous_prime_gap: 128
prime_density: '4.14640000'
isolated_primes:
is_isolated_prime: 'true'
combined_gap: 254
previous_prime_gap: 128
next_prime_gap: 126
isolated_prime_density: '4.14640000'
birth_certificate: >-
2019-03-23 04:37:54: server sitka processed 179 838
computations in 8.0284937062072 micro-seconds using 2 x
2.8 GHz Quad-Core Intel Xeon CPUs
'403':
description: Forbidden
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description: Not Found
headers:
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example: Sat, 11 Sep 2021 23:26:12 GMT
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content:
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schema:
type: object
examples:
example-0:
summary: error (minimum_combined_prime_gap too small)
value:
error: >-
Minimum combined prime gap value too small; has to be
between 200 and 524
example-1:
summary: error (minimum_combined_prime_gap too big)
value:
error: >-
Minimum combined prime gap value too big; has to be
between 200 and 524
example-2:
summary: error (alpha minimum_combined_prime_gap)
value:
error: >-
Minimum combined prime gap value not a number; has to be
between 200 and 524