ElevenSmooth Introduction
M(3326400) = 2 |

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 2^{n}-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)=2^{713}-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.

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.

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.