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?



Smallest collection of bases for prime testing of 64 bit numbers?
According to <http://miller-rabin.appspot.com/>, the 7-element set {2, 325, 9375, 28178, 450775, 9780504, 1795265022} works for 64-bit integers.


