Math::Prime::Util::PrimalityProving - Primality proofs and certificates


Version 0.73



Routines to support primality proofs and certificate verification.



Given a positive number n as input, performs a full factorization of n-1, then attempts a Lucas test on the result. A Pratt-style certificate is returned. Note that if the input is composite, this will take a very long time to return.


Given a positive number n as input, performs a partial factorization of n-1, then attempts a proof using theorem 5 of Brillhart, Lehmer, and Selfridge's 1975 paper. This can take a long time to return if given a composite, though it should not be anywhere near as long as the Lucas test.


Takes as input a Perl structure certificate, used by Math::Prime::Util from version 0.26 through 0.29, and converts it to a multi-line text certificate starting with "[MPU - Primality Certificate]". This is the new format produced and processed by Math::Prime::Util, Math::Prime::Util::GMP, and associated tools.


Takes a MPU primality certificate and verifies that it does prove the primality of the number it represents (the N after the "Proof for:" line). For backwards compatibility, if given an old-style Perl structure, it will be converted then verified.

The return value will be 0 (failed to verify) or 1 (verified). A result of 0 does not indicate the number is composite; it only indicates the proof given is not sufficient.

If the certificate is malformed, the routine will carp a warning in addition to returning 0. If the verbose option is set (see "prime_set_config") then if the validation fails, the reason for the failure is printed in addition to returning 0. If the verbose option is set to 2 or higher, then a message indicating success and the certificate type is also printed.

A later release may add support for Primo certificates, as all the method verifications are coded.




Dana Jacobsen <>


Copyright 2012-2013 by Dana Jacobsen <>

This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.