Primality test

A primality test is a method (or algorithm) to find out if a certain number is a prime number. Cryptography uses prime numbers, and needs to test if a certain number is prime. The official proof of a prime is through its primality certificate.

Simple methods

• Sieve of Eratosthenes: Determine if there is a number (between 2 and n, the number to test) that divides n, without a rest
• Wilson's theorem (inefficient): $(p-1)!$ evaluates to -1 mod p where p is the candidate prime number

Better methods

• Fermat's primality test
• Miller-Rabin primality test

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