ElevenSmooth Introduction
Searching for factors of the Mersenne number

M(3326400) = 23326400-1

  Click for a slide show
introduction to
Distributed Computing in
general and ElevenSmooth
in particular.

ElevenSmooth is a distributed computing project searching for prime factors of M(3326400). Mersenne numbers, numbers of the form 2n-1, are named for the French mathematician Marin Mersenne (1588-1648). Prime factors of Mersenne numbers are occasionally useful to mathematicians. For example, NFSNET factored M(713)=2713-1 to help in Richard Brent and Paul Zimmerman's research into primitive trinomials. Primitive trinomials have applications in cryptography, coding theory, and random number generation. Factors of Mersenne numbers are also central to the study of covering sets for Sierpinski, Riesel, and Brier numbers. The Cunningham Project has been collecting Mersenne factors (and other factors) since 1925. There is enough interest in Mersenne factors that Will Edgington updates the file of known factors every few weeks on his web site.

But mostly we do this for the fun; fun from the small thrill of finding factors that nobody has ever seen before, fun from contributing to a generations long endeavor, fun from the satisfaction of using idle computers, and fun from the online comraderie.

What We Do and How to Join

We apply the Elliptical Curve Method (ECM) to factor known composite factors of M(3326400). The composite factors are stored in a server. A client program runs on our computers. The client program contacts the server across the internet to get a task - a particular composite number. The client program then starts the ECM factoring program on our computers, running at low priority. After thirty minutes (adjustable), the client program contacts the server again, reports the results, and gets another assignment. See the FAQ page for more information.

To participate, you download the ECM factoring program and the ECMclient program, edit the configuration file to identify yourself, and start the ECMclient program. See the Download page for more information.

Other Methods We Use

We also use P-1 and P+1 factoring on the composites. At present this work is not distributed

Sometimes we identify large Probable Primes (PRPs). Then we use an Eliptical Prime Proving (EPP) program such as Primo to prove these numbers are prime.

We have a special project underway that uses the Prime95 program to perform ECM testing on many numbers simultaneously. The first stage of this special project found forty new factors. The special project is presently open to people who have completed at least one week of ECM work.