A primality test is an algorithm for determining whether an input number is prime. It is important to note the difference between primality testing and integer factorization — factorization is, as of 2006, a computationally hard problem, whereas primality testing, as shown below, is comparatively easy.

Naïve methods

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The simplest primality test is as follows: Given an input number n, we see if any integer m from 2 to n-1 divides n. If n is divisible by any m then n is composite, otherwise it is prime.

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