## Nearest Prime Number Finder

## Answers to Questions

### How to calculate the closest prime number?

No formula can find the **nearest prime** number of another given number. dCode uses algorithms based on probabilistic primality tests for numbers higher 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, ... 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, ... 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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