Advanced Methods for Factoring Integers

Version 1.5.4

Stefan Kohl


FactInt is a GAP 4 package which provides implementations of the following methods for factoring integers:

FactInt also makes use of Richard P. Brent's tables of known factors of integers of the form bk+/-1 for `small' b. The code for accessing these tables has been contributed by Frank Lübeck.

The ECM is suited best for finding factors which are neither too small (i.e. have less than about 12 decimal digits) nor too close to the square root of the number to be factored. The MPQS is designed for factoring products of two primes of comparable orders of magnitude. CFRAC is the historical predecessor of the MPQS. Pollard's p-1 and Williams' p+1 are useful for finding factors p such that all prime factors of p-1 resp. p+1 are `small', e.g. smaller than 1000000. All factoring methods implemented in this package are probabilistic. In particular the time needed by the ECM depends highly on the actual - good or bad - luck.

FactInt provides a general-purpose factorization routine which uses an appropriate combination of the methods mentioned above, the Pollard Rho routine which is implemented in the GAP Library and a variety of tricks for special cases to obtain a good average performance for `arbitrary' integers. At the user's option, FactInt provides detailed information about the progress of the factorization process.

FactInt is published / redistributed on the GAP website here.

Download, Manual and Examples

If you have problems with this package, wish to make comments or suggestions, or if you find bugs, please send e - mail to Stefan Kohl.