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

Question

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.

score 2 · Accepted Answer · answered Mar 05 '14 at 10:56

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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).

answered Mar 05 '14 at 10:56

Brett Hale

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score 0 · Answer 2 · answered Mar 05 '14 at 10:00

0

According to OEIS, use of witnesses up to 23 suffices for numbers up to 3825123056546413051

answered Mar 05 '14 at 10:00

kinokijuf

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user448810 · Answer 3 · 2014-03-05T14:51:21.420

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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.

edited Mar 05 '14 at 14:51

answered Mar 05 '14 at 13:33

user448810

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This should be a comment, not an answer. – kinokijuf Mar 05 '14 at 16:34

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

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