A primality test is an algorithm for determining whether an input number is prime. Amongst other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not. Factorization is thought to be a computationally difficult problem, whereas primality testing is comparatively easy (its running time is polynomial in the size of the input). Some primality tests prove that a number is prime, while others like Miller–Rabin prove that a number is composite. Therefore we might call the latter compositeness tests instead of primality tests.
Read more about Primality Test: Naive Methods, Probabilistic Tests, Fast Deterministic Tests, Complexity, Number-theoretic Methods
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“Tried by a New England eye, or the more practical wisdom of modern times, they are the oracles of a race already in its dotage; but held up to the sky, which is the only impartial and incorruptible ordeal, they are of a piece with its depth and serenity, and I am assured that they will have a place and significance as long as there is a sky to test them by.”
—Henry David Thoreau (1817–1862)