Hello. Does anyone know any (non-pseudo) primality tests with complexity better than O(√n)? The thing is, I was reading about a simple one that has O(∛n) or O(∜n) complexity, but now I just can't find it! I remember that the core idea was checking some divisors (not up to square root) and then analyzing cases of prime decomposition. Thank you.
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Miller–Rabin primality test is the fastest algorithm, but it is not deterministic. You need to run the test multiple times to reduce the failure probability.