A heuristic test for prime numbers. It repeatedly checks if the number being tested, n, is pseudoprime to a randomly chosen base, a, and there are only trivial square roots of 1, modulo n. In other words, n is surely composite if a^n-1 ≠ 1 (mod n), where 0 < a < n. Some composites may be incorrectly judged to be prime.

For k repetitions, the chance of incorrectly judging an odd integer greater than 2 to be prime is 2^-k. For randomly chosen large integers, a small number of repetitions, say 3, is enough.