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primesprimality-test

What witnesses do i need for Rabin-Miller test for numbers up to 10¹⁸?


What set of witnesses is sufficient for the Miller-Rabin test to be correct for all numbers up to 10¹⁸? I know that use of primes up to 17 as witnesses suffices for n < 341550071728321.


Solution

  • According to this record page, the set of 7 SPRP bases: {2, 325, 9375, 28178, 450775, 9780504, 1795265022} is sufficient for a deterministic test to at least n = 2^64 ( > 10^19).