Ruby

Interesting. We might as well always return the correct result, i.e. apply the fast algorithm for integers < 318,665,857,834,031,151,167,461 and the slow algorithm for larger ones. Would you care to modify your patch?

marcandre (Marc-Andre Lafortune) wrote:

Interesting. We might as well always return the correct result, i.e. apply the fast algorithm for integers < 318,665,857,834,031,151,167,461 and the slow algorithm for larger ones. Would you care to modify your patch?

If you were to use the existing algorithm on 318,665,857,834,031,151,167,461 you'd need Math.sqrt(318665857834031151167461 ) / 30.0 = 18_816_832_235 loop iterations.. Its not worth falling back given how inefficient the existing function is at that magnitude.

It can fall back to APR-CL primality test when Miller-Rabin does not work. In my personal opinion, it would be best to keep prime.rb simple because it is a hobby library.

You may be interested in my gem: https://github.com/mame/faster_prime

On second thought, I think Marc is right, we can't ruin someones day with a composite without a warning that theres a non-zero probability of it being incorrect so I will update......

I think it would be interesting to expose the algorithm for larger numbers. So you could have miller_rabin which allows any integer, and prime? which checks the value and either call miller_rabin or raise ArgumentError.

Dan0042 (Daniel DeLorme) wrote in #note-15:

I think it would be interesting to expose the algorithm for larger numbers. So you could have miller_rabin which allows any integer, and prime? which checks the value and either call miller_rabin or raise ArgumentError.

Unforunately Miller-Rabin is not a deterministic test for arbitrarily large n - its only the work in the paper https://arxiv.org/pdf/1509.00864.pdf that allows us to provide functionality up to a bound.

steveb3210 (Stephen Blackstone) wrote in #note-16:

Unforunately Miller-Rabin is not a deterministic test for arbitrarily large n - its only the work in the paper https://arxiv.org/pdf/1509.00864.pdf that allows us to provide functionality up to a bound.

Yes, I know, that was my point. Maybe I want to know if arbitrarily large N is prime while accepting a probability of error of 4**(-k); then I could use miller_rabin(k). And the prime? method uses a bounds check and miller_rabin(13) to produce a deterministic result.

BTW your implementation appears to be off by one. It should be: if self >= 3317044064679887385961981 then raise ArgumentError. You could also slightly reduce the runtime for small numbers by using return list.include?(self) if self <= list.last before the loop, instead of checking inside the loop.