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Next Prime Number

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)

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Next Prime Number -

Tag(s) : Arithmetics

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# Next Prime Number

## Next Prime Number Search

### What is the next prime number? (Definition)

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.

### How to calculate the next prime number?

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).

### How to find smallest primes with n digits?

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)

### What are twin primes numbers?

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.

## Source code

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!
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## Cite dCode

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 2022-09-30, https://www.dcode.fr/next-prime-number

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