Tool to find the closest prime number of a number, the prime number nearest to a given number also called closest Prime function

Closest Prime Number - dCode

Tag(s) : Arithmetics

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For a given number $ N $, the nearest prime number is the prime number that minimizes its distance from $ N $ (whose difference between itself and $ N $ is minimal, such that there are no other closer primes).

No mathematical formula can find the nearest prime number of another given number. dCode uses algorithms based on probabilistic primality tests for numbers greater or lower than the number requested, and then checks it via deterministic algorithms.

__Example:__ The closest prime number to `100` is `101`

__Example:__ The nearest prime number to `1000` is `997` (the next is `1009`)

__Example:__ The closest prime number to `10000` is `10007`

If the next prime number and the previous prime number are at the same distance, dCode returns the next prime number.

Two prime numbers are called twins if their difference is 2 (the nearest prime number is at a distance of 2 units).

__Example:__ 5 and 7 are twins because $ 7-5 = 2 $

The OEIS lists 2 series of numbers:

A051697: $ 2, 2, 2, 3, 3, 5, 5, 7, 7, 7, 11, 11, 11, 13, \dots $ which for any integer N associates its nearest prime number (the smallest in the case of a tie)

A077018: $ 2, 2, 2, 3, 5, 5, 7, 7, 7, 11, 11, 11, 13, 13, \dots $ which for any integer N associates its nearest prime number (the largest in case of a tie)

The 2 sequences are identical except for the number `3` which appears twice in the first sequence but only once in the second one.

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Cite as source (bibliography):

*Closest Prime Number* on dCode.fr [online website], retrieved on 2023-01-29,

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

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