Request a random prime number value isolated with a minimum combined prime gap of at least 200, and as much as 500, and even assess the level of isolation and % chance to randomly find that number within a million composite numbers!

GET   get-isolated-random-prime (paid)

http://api.prime-numbers.io/get-isolated-random-prime.php?key=YOUR_API_KEY&include_explanations=<boolean>&include_prime_types_list=<boolean>&minimum_combined_prime_gap=<number>&language=<string>
AUTHORIZATION API Key
This request is using the API Key from Prime Numbers API collection in thePime Numbers API environment

PARAMS

key
YOUR_API_KEY

(Required) your API key
include_explanations
<boolean>

includes the full explanations for each item if true (default is false)
include_prime_types_list
<boolean>

includes the full prime types list for each item if true (default is false)
minimum_combined_prime_gap
<number>

the total number of neighbouring composite numbers on the right and 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)
language
<string>

show the output translated into that language (it can be english, mandarin, hindi, spanish, french, german, italian, japanese, russian) (default is english)


Success (no query params)


Example Request 
curl --location --request GET 'http://api.prime-numbers.io/get-isolated-random-prime.php?key=YOUR_API_KEY&language=english'
Example Response

200 OK


{
    "random_prime_number_value": 14702690531,
    "minimum_combined_prime_gap_value": 200,
    "base_conversions": {
        "binary_value": "1101101100010110010100000011100011",
        "senary_value": "10430533403415",
        "hexa_value": "36c5940e3"
    },
    "previous_prime_gap": 120,
    "prime_density": "4.28280000",
    "isolated_primes": {
        "is_isolated_prime": "true",
        "combined_gap": 252,
        "previous_prime_gap": 120,
        "next_prime_gap": 132,
        "isolated_prime_density": "0.00640000"
    },
    "birth_certificate": "2019-03-29 12:41:27: server mac-server processed 121 255 computations in 5.052277149375 micro-seconds using 2 x 3 GHz Quad-Core Intel Xeon CPUs"
}


Success (with explanations, prime_types, and minimum_combined_prime_gap)


Example Request 
curl --location --request GET 'http://api.prime-numbers.io/get-isolated-random-prime.php?key=YOUR_API_KEY&include_explanations=true&include_prime_types_list=true&minimum_combined_prime_gap=500&language=english'
Example Response

200 OK


{
    "random_prime_number_value": 85057565909,
    "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": "1001111001101110100110111010011010101",
        "binary_value_explanation": "prime number base-2 (binary value), useful for cryptography and cryptocurrency",
        "senary_value": "103024102455205",
        "senary_value_explanation": "prime number base-6 (senary value), useful for mathematical research",
        "hexa_value": "13cdd374d5",
        "hexa_value_explanation": "prime number base-16 (hexa value), useful for cryptography and cryptocurrency"
    },
    "previous_prime_gap": 406,
    "previous_prime_gap_explanation": "how many successive prime and composite numbers are between this prime and the previous one",
    "prime_density": "3.96810000",
    "prime_density_explanation": "how many prime numbers (%) can be found in this million composite numbers (between 85 057 000 000 and 85 058 000 000)",
    "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 0.008086097174%",
        "combined_gap": 520,
        "previous_prime_gap": 406,
        "next_prime_gap": 114,
        "isolated_prime_density": "0.00960000",
        "isolated_prime_density_explanation": "how many chances (%) to randomly find an isolated prime number in this million composite numbers (between 85 057 000 000 and 85 058 000 000)"
    },
    "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 85 057 000 000 and 85 058 000 000)",
        "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": "0.41460000",
        "twin_density_explanation": "how many twin prime numbers (%) can be found in this million composite numbers (between 85 057 000 000 and 85 058 000 000)",
        "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": "0.41860000",
        "cousin_density_explanation": "how many cousin prime numbers (%) can be found in this million composite numbers (between 85 057 000 000 and 85 058 000 000)",
        "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": "0.72490000",
        "sexy_density_explanation": "how many sexy prime numbers (%) can be found in this million composite numbers (between 85 057 000 000 and 85 058 000 000)",
        "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 85 057 000 000 and 85 058 000 000)",
        "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 85 057 000 000 and 85 058 000 000)",
        "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 85 057 000 000 and 85 058 000 000)",
        "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 85 057 000 000 and 85 058 000 000)",
        "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 85 057 000 000 and 85 058 000 000)"
    },
    "birth_certificate": "2020-11-17 17:27:26: server ferdinand processed 291 646 computations in 8.294832273952 micro-seconds using 2 x 2.93GHz Hexa-Core Intel Xeon CPUs",
    "birth_certificate_explanation": "how many computations, how much time and what computer power was used to find this prime number"
}


Error (no key)


Example Request 
curl --location --request GET 'http://api.prime-numbers.io/get-isolated-random-prime.php?key=&language=english'
Example Response

403 Forbidden


{
    "error": "please include the api key in your query"
}


Error (minimum_combined_prime_gap too small)


Example Request 
curl --location --request GET 'http://api.prime-numbers.io/get-isolated-random-prime.php?key=YOUR_API_KEY&minimum_combined_prime_gap=150&language=english'
Example Response

404 Not Found


{
    "error": "Minimum combined prime gap value too small; has to be between 200 and 524"
}


Error (minimum_combined_prime_gap too big)


Example Request 
curl --location --request GET 'http://api.prime-numbers.io/get-isolated-random-prime.php?key=YOUR_API_KEY&minimum_combined_prime_gap=600&language=english'
Example Response

404 Not Found


{
    "error": "Minimum combined prime gap value too big; has to be between 200 and 524"
}


Error (alpha minimum_combined_prime_gap)


Example Request 
curl --location --request GET 'http://api.prime-numbers.io/get-isolated-random-prime.php?key=YOUR_API_KEY&minimum_combined_prime_gap=aaa&language=english'
Example Response

404 Not Found


{
    "error": "Minimum combined prime gap value not a number; has to be between 200 and 524"
}