Fastest algorithm for primality test [closed]

Answer 1

I would suggest the GNU MP library that uses the Miller-Rabin algorithm. I have used it for a few months and it's very fast.

Specifically, the function mpz_probab_prime_p does this, you can also use another function mpz_nextprime to find the next prime number greater than a number. I can post code samples if you would like.

Answer 2

Cobbal and grokus are right. The Miller-Rabin test is the most useful of the available algorithms. Yes, it is probabilistic, but really shouldn't scare you off. The test is the most widely used for practical purposes.

Note that the probability of false positives (there are no false negatives) can be made arbitrarily small by repeating the test.

Answer 3

Fastest would probably be to look it up in a precomputed list of primes. See here for example, they have up to 2^43112609-1 (largest known prime).

Answer 4

A Miller-Rabin test to the seven bases 2, 325, 9375, 28178, 450775, 9780504, 1795265022 has been proved by Jim Sinclair to deterministically test if a number less than 2^64 is prime. See http://miller-rabin.appspot.com/.

Answer 5

I came up with a really good algorithm, that is much faster than checking all the divisors - which of course also lets me crack public key encryption.

Hang on - I just need to close the window, there are all these black helicopters overhead ........

(Or look at How can I test for primality?)

Answer 6

Take a look at my answer here:

how to test a prime number 1000 digits long?

The test is very fast. If you are working in the 64-bit or smaller range, you can throw in a GCD with 30030 to save a bit of time for the majority of numbers.