TITLE: Smallest collection of bases for prime testing of 64 bit numbers?
QUESTION [13 upvotes]: I know that no number less than 64 bits will fail the Miller-Rabin tests for all of the first 12 primes.  That is, those 12 tests will provide a fully deterministic primality test for all 64 bit numbers.  (See http://oeis.org/A014233).  I also know that for 32 bit numbers, it suffices to apply the Miller-Rabin tests for the three bases 2, 7 and 61.  (See http://primes.utm.edu/prove/merged.html).  Is there a very small list of possible bases (other than the first 12 primes), which will provide a fully deterministic test for 64 bit primes?

REPLY [12 votes]: According to http://miller-rabin.appspot.com/, the 7-element set {2, 325, 9375, 28178, 450775, 9780504, 1795265022} works for 64-bit integers.