Re^2: optimizing the miller-rabin algorithm

[syphilis]

The way I read the algorithm ..., you're looping too much in your middle loop. I believe you're supposed to choose a fixed accuracy k, and then a random set of k bases. You're using *all* numbers less than n as a base, and that is way too strong, especially for very large numbers, for which this algorithm is designed.

Yes, that's pretty much right. Furthermore, for any number less than 341550071728322, if the Miller-Rabin test doesn't return "composite" for any of the bases 2, 3, 5, 7, 11, 13 and 17, then the number in question is proven to be prime. For numbers less than 1373653 it is sufficient to test only for bases 2 and 3. See http://primes.utm.edu/prove/prove2_3.html

For large numbers Math::BigInt's bmodpow (pure perl) function is just way too slow. You'll be wanting to use something like Math::Pari or Math::GMP (as rhesa has suggested).

Cheers,
Rob