Ernst Home: Great Internet Mersenne Prime Search

The Great Internet Mersenne Prime Search

Give us your spare CPU cycles and earn a chance to make math history! The Electronic Freedom Foundation is offering a US$100,000 prize for the discovery of the first known ten-million digit prime number. A GIMPS member found the last such prize number. Here's your chance to join the lottery, and contribute to mathematics research at the same time.

4 out of 5 NASA scientists agree: aside from global warming, GIMPS is the hottest thing out there, and that makes it very cool.

Mersenne primes are named after 17th-century minim friar Marin Mersenne, and are numbers of the form M(p) = 2^p-1, where the binary exponent p must itself be prime for the number to have a chance at being prime (most aren't, e.g. 2¹¹-1 = 23*89 and 2⁹⁹⁷-1 = 1675608 1651408481 9488737767 9762631504 0509519155 4732902607 * 7993 4306053602 2229286093 6960123884 0619880168 4662721375 7686887976 0059300256 3860297371 2891518592 8789446877 5962208410 6508783413 8557781773 6702215887 8920741413 7008681823 0141043917 8049533828 0826515131 6094560701 8874830040 9784532283 7881664735 8334681553). Started in 1995 by Luke Welsh (co-discoverer of the Mersenne prime M110503) and retired Florida programmer George Woltman, GIMPS is arguably the most successful distributed computing project in history. The SETI folks have more computers, but so far have found lots of static. GIMPS, on the other hand, has discovered the seven largest known Mersenne primes (each of which was/is the largest known prime of any type at the time of its discovery), including the most recent, the 7-million-plus digit monster 2^25964951-1. Admittedly the stakes are rather higher with SETI, but from the standpoint of recruiting volunteers worldwide and then (more importantly) keeping them on board for the long haul, it's nice to have some actual successes at fairly regular intervals. Also, the software available to GIMPSers makes better use of the computer CPU than that of the SETI@HOMErs, partly because it doesn't waste precious cycles generating eye candy (i.e. fancy graphics and whoopee-cool screen savers).

Related links:

Here's the Mlucas code I wrote to test Mersenne numbers for primality, optimized for RISC-style workstations.
Marin Mersenne (Encyclopedia Britannica entry)
Pierre (de) Fermat (Encyclopedia Britannica entry)
And speaking of Monsieur Fermat, here's a paper about the famous number sequence named after him.
Other Mersenne-prime-related Britannica links.

http://hogranch.com/mayer/gimps.html -- Last Revised: 21 May 2005
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