Tool to search for prime numbers, such as the prime following a given number (next), or the nth prime number greater than a given number (Next Prime Function)

Next Prime Number - dCode

Tag(s) : Arithmetics

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For a given number $ N $, the next prime number is the smallest number strictly greater than $ N $ which is a prime number. As there are an infinity of prime numbers, this number always exists.

There is no formula on how to find the next prime number. dCode uses an algorithm that performs a probabilistic primality test (Miller-Rabin test) on each of the numbers greater than or equal to the number requested, then check it with a deterministic test.

__Example:__ The first prime number following `1000` is `1009`.

__Example:__ The 10th prime number after `100` is `149` (so there are 9 prime numbers between 101 and 148)

The number must be a positive real number (the decimal numbers are accepted).

The first prime number following $ 10^{n-1} $ is a number with $ n $ digits which is the smallest n-digit prime number.

__Example:__ 2, 11, 101, 1009, 10007, 100003, etc. here (link)

A prime number and the next prime number are said to be twins if their difference is 2.

__Example:__ 11 and 13 are twin primes because 13-11 = 2.

dCode retains ownership of the "Next Prime Number" source code. Except explicit open source licence (indicated Creative Commons / free), the "Next Prime Number" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Next Prime Number" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Next Prime Number" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!

Reminder : dCode is free to use.

The copy-paste of the page "Next Prime Number" or any of its results, is allowed as long as you cite dCode!

Cite as source (bibliography):

*Next Prime Number* on dCode.fr [online website], retrieved on 2023-02-08,

next,following,prime,number,list,greater

https://www.dcode.fr/next-prime-number

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