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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Closest Prime Number
Nearest Prime Number Finder
Answers to Questions (FAQ)
What is the closest prime number? (Definition)
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).
How to calculate the closest prime number?
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.
What are twin primes numbers?
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 $
What is the sequence of closest prime numbers to N?
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.
Source code
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