October 9th 2007

Cunningham Project

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1. Introduction

The Cunningham project was one of the first attempts to systematically tabulate factorizations of large numbers. Originally, only numbers of the form an +/- 1 with a = 2, 3, 5, 6, 7, 10, 11, 12 and n <= 1200 have been considered, but with increasing computer power also many numbers for n > 1200 have been factorized since then.

There is an official Cunningham project site which is updated regulary.

2. Elliptic Curves

I have been using GMP-ECM to run some elliptic curves on yet not fully factored Mersenne numbers Mn = 2n - 1. Each elliptic curve is one job. These jobs are queued on lowest priority into a network of up to 52 computers, which is normally used for speech recognition research. Elliptic curves can only run when CPU-time is free, which is usually about 30% of the total capacity. Summary of factors and completed work: To improve throughput I have been performing step 1 of some elliptic curves with George Woltmans Prime95. The disadvantage is, that I can run Prime95 only on the few CPUs where I have administration rights.

The overall status of factorization of Mersenne numbers are summarized at the GIMPS status page.

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