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Advanced Methods for Factoring Integers


18 February 2018

Stefan Kohl

Alexander Konovalov
School of Computer Science
University of St Andrews
Jack Cole Building, North Haugh,
St Andrews, Fife, KY16 9SX, Scotland


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 ± 1. FactInt is completely written in the GAP language and contains / requires no external binaries. It needs GAPDoc 1.6 [LN17] or higher. FactInt must be installed in the pkg subdirectory of the GAP distribution.


© 1999 - 2017 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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