On Sat, 6 Sep 2014 12:53:16 +0200, Manolo Martínez wrote: > On 09/06/14 at 08:38pm, Steven D'Aprano wrote: >> But even that's not how the specialists do it. If you want to check whether >> (say) 2**3000+1 is prime, you don't want to use trial division at all... > > When I was interested in these things, specialists would use the [number > field sieve](https://en.wikipedia.org/wiki/General_number_field_sieve).
No, one uses the number field sieve to *factor* large numbers. To test for primality, one uses simple tests like Fermat's test (x**(n-1)%n == 1, for many different x) or the slightly more complex Miller-Rabin test. These probabilistic primality tests can prove that a number is composite, but they can't actually *prove* that a number is prime. For that, you need a more complex test that is beyond my ken as a cryptologist. -- To email me, substitute nowhere->runbox, invalid->com. -- https://mail.python.org/mailman/listinfo/python-list
