gmp-ecm

Factor integers using the Elliptic Curve Method

gmp-ecm is a free implementation of the Elliptic Curve Method (ECM) for integer factorization. The original purpose of the ECMNET project was to make Richard Brent's prediction true, i.e. to find a factor of 50 digits or more by ECM. This goal was attained on September 14, 1998, when Conrad Curry found a 53-digit factor of 2^677-1 c150 using George Woltman's mprime program. The new goal of ECMNET is now to find other large factors by ecm, mainly by contributing to the Cunningham project, most likely the longest, ongoing computational project in history according to Bob Silverman. A new record was set by Nik Lygeros and Michel Mizony, who found in December 1999 a prime factor of 54 digits using GMP-ECM. See http://www.loria.fr/~zimmerma/records/ecmnet.html for more information about ecmnet. This package provides the command line utility.

sagemath

Open Source Mathematics Software, free alternative to Magma, Maple, Mathematica, and Matlab

ecm

prepares CD image files so they compress better

The ECM format allows you to reduce the size of a typical CD image file (BIN, CDI, NRG, CCD, or any other format that uses raw sectors). It works by eliminating the Error Correction/Detection Codes (ECC/EDC) from each sector whenever possible. The encoder automatically adjusts to different sector types and automatically skips any headers it encounters. Since the data skipped is nearly impossible to compress with traditional tools, the resulting ECM file will compress far better than the raw CD image.