问题
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.
回答1:
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).
回答2:
According to OEIS, use of witnesses up to 23 suffices for numbers up to 3825123056546413051
回答3:
If you're willing to use a Baillie-Wagstaff test instead of a Miller-Rabin test, it has been certified to be error-free in classifying primes up to 2^64. The coding is not much more complicated, the function executes more quickly than a Miller-Rabin test, and there are no known errors of classification.
来源：https://stackoverflow.com/questions/22194207/what-witnesses-do-i-need-for-rabin-miller-test-for-numbers-up-to-10%c2%b9%e2%81%b8