# leto/math--primality

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 =head1 ROADMAP =head2 References * Description of PARI primality algorithms: http://www.math.u-bordeaux.fr/~belabas/pari/doc/faq.html =head2 To be Done * More user documentation, explain the general idea of the algorithm used =head2 Hairy Details * Math::GMPz implements all the hairy details of GMP =head2 Other Possibilities =head2 Already Done * Port iBPSW from spec/bpsw/bpsw1.c is_prime(\$N) <==> iBPSW(N,1) This is basically trial division, followed by a is_strong_pseudoprime(), followed by a is_strong_lucas_pseudoprime() There are many optimizations to made for small arguments Main function: is_prime(), to replace Math::PARI::is_prime() It may take optional arguments for power-users, but we want to have a really simple function for people to call like this: is_prime(\$x) ? foo() : bar(); which "does what I mean." ** next_prime() This function is merely a wrapper around is_prime(), which takes a starting number and increments it until is_prime() returns true and then returns that number. This should only require a small number of tests, most of the work is in making the necessary components of is_prime(). * Port iMillerRabin from spec/bpsw/trn.c , this will be is_strong_pseudoprime() * implement base b pseudoprime test, a.k.a n is in psp(b) this is is_pseudoprime() * Port iStrongLucasSelfridge(mpz_t) from spec/bpsw/trn.c , this will be is_strong_lucas_pseudoprime() =cut =head2 References * Description of PARI primality algorithms: http://www.math.u-bordeaux.fr/~belabas/pari/doc/faq.html
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