Smallest collection of bases for prime testing of 64 bit numbers?

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?

• Is there a particular reason to believe that the first 12 primes are sufficient to cover 64-bit primes? From the OEIS list we can only deduce that the 11ish set fails at 61.7 bits; the 12ish set might fail very soon after for all we know – DarthGizka Nov 10 '14 at 14:54
• The OEIS entry explicitly states a(12) > 2^64. – Emil Jeřábek supports Monica Nov 12 '14 at 13:38

• The conventions used by the author of miller-rabin.appspot.com are described in priv.ckp.pl/wizykowski/sprp.pdf , though not particularly clearly. You are supposed to test all bases not divisible by $n$. Note that the definition of base-$a$ strong pseudoprimes really only makes good sense for $(n,a)=1$. The commonly presented randomized algorithm, restricting the bases to $1<a<n$, exploits the unrelated fact that any common factor of $n$ and $a$ will make $n$ composite, however this is not literally true for $a\ge n$, one must exclude multiples of $n$. – Emil Jeřábek supports Monica Jul 30 '14 at 10:48