GIMPS is also involved in trying to factor numbers of the form 2N-1 and 2N+1 using either the P-1 method or the Elliptic Curve Method (ECM). You can win cash awards for factoring Fermat numbers, or gain a small footnote in math history by finding a new factor for the Cunningham tables, or improve Paul Leyland's table for Mersenne numbers below 10,000, or improve the Mersenne status page by moving an exponent from the "two LL tests" column to the "factored" column.
To help in this factoring effort, you will need version 16.4 or later of the program. Then download the files of known factors lowm.txt and lowp.txt. Finally, pick a few exponents from the tables on the web pages below and run a few curves. When done, email the results.txt file to me and I will add your curves to the counts below. The program was adapted from Richard Crandall's free program and uses an assembly language implementation of his irrational base discrete weighted transforms algorithm for superior performance. Several important improvements came from Paul Zimmermann and Peter Montgomery. Zimmermann's program is ideal for non-PC platforms.
Each web page below contains a table indicating how much ECM factoring has been done on a number. ECM factoring consists of trying a n