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Advanced Methods for Factoring Integers

Version 1.5.3

June 16, 2011

Stefan Kohl
Department of Mathematics
University of Vlora
Lagjja: Pavaresia
Vlore / Albania


This package for GAP 4 provides a general-purpose integer factorization routine, which makes use of a combination of factoring methods. In particular it contains implementations of the following algorithms:

It also contains code by Frank Lübeck for making use of Richard P. Brent's tables of factors of integers of the form b^k pm 1. FactInt is completely written in the GAP language and contains / requires no external binaries. It needs GAPDoc 1.0 [LN07] or higher. FactInt must be installed in the pkg subdirectory of the GAP distribution.


© 1999 - 2011 by Stefan Kohl.

FactInt is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.

FactInt is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

For a copy of the GNU General Public License, see the file GPL in the etc directory of the GAP distribution or see


I would like to thank Bettina Eick and Steve Linton for their support and many interesting discussions.


1 Preface
2 The General Factorization Routine
3 The Routines for Specific Factorization Methods
4 How much Time does a Factorization take?

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