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Mersenne Prime Search

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December 2005: New Mersenne Prime! Pages available in Chinese, Danish, Dutch, French, German, Italian, and Spanish. Warning: These translations may not be up-to-date - use AltaVista as necessary. 43rd Known Mersenne Prime Found!! On December 15, 2005, Dr. Curtis Cooper and Dr. Steven Boone, professors at Central Missouri State University, discovered the 43rd Mersenne Prime, 230,402,457-1. The CMSU team is the most prolific contributor to the GIMPS project. The discovery is the largest known prime number.

The new prime is 9,152,052 digits long. This means the Electronic Frontier Foundation $100,000 award for the discovery of the first 10 million digit prime is still up for grabs! The new prime was independently verified in 5 days by Tony Reix of Bull S.A. in Grenoble, France using 16 Itanium2 1.5 GHz CPUs of a Bull NovaScale 6160 HPC at Bull Grenoble Research Center, running the Glucas program by Guillermo Ballester Valor of Granada, Spain.

Dr. Cooper joined GIMPS over 7 years ago with colleague Dr. Vince Edmondson. Edmondson was instrumental in the campus-wide effort until he passed away in 2003. Cooper, Boone, and CMSU truly earned this discovery, diligently coordinating over 700 PCs!

However, Dr. Cooper and Dr. Boone could not have made this discovery alone. In recognition of contributions made by tens of thousands GIMPS volunteers, credit for this new discovery goes to "Cooper, Boone, Woltman, Kurowski, et al". The discovery is the ninth record prime for the GIMPS project. Join now and you could find the next record-breaking prime! You could even win some cash.

Perfectly Scientific, Dr. Crandall's company which developed the FFT algorithm used by GIMPS, will make a poster you can order containing the entire 9.1 million digit number. It is kind of pricey because accurately printing an over-sized poster in 1-point font is not easy! This makes a cool present for the serious math nut in your family.

For more information on this prime discovery read the full press release (not yet available).

Mersenne Wiki Created From the good folks that brought you the Mersenne Forums comes the Mersenne Wiki. Browse the Wiki to learn more about GIMPS and Mersenne Primes. If you're already knowledgeable, then consider contributing to the Wiki.

42nd Known Mersenne Prime Found! On February 18, 2005, Dr. Martin Nowak from Germany, found the new largest known prime number, 225,964,951-1. The prime number has 7,816,230 digits! It took more than 50 days of calculations on Dr. Nowak's 2.4 GHz Pentium 4 computer. The new prime was independently verified in 5 days by Tony Reix of Grenoble, France using a 16 Itanium CPU Bull NovaScale 5000 HPC running the Glucas program by Guillermo Ballester Valor of Granada, Spain. A second verification was completed by Jeff Gilchrist of Elytra Enterprises Inc. in Ottawa, Canada using 15 days of time on 12 CPUs of a Compaq Alpha GS160 1.2 GHz CPU server at SHARCNET.

Dr. Martin Nowak, an eye surgeon in Michelfeld, Germany learned of GIMPS in April 1999 when he read an article in his newspaper, the "Frankfurter Allgemeine Zeitung". Dr. Nowak, a math hobbyist, started with one PC and as his practice grew so did his participation in GIMPS. Six years later, he has 24 computers doing calculations for GIMPS -- and one Mersenne Prime to his credit!

For more information on this prime discovery read the full press release.

Version 24 of prime95/mprime released Version 24 is now available. All users except those using older intel architectures (Pentium 3 and earlier) should get a nice speedup. Go to the download page to upgrade.

NFSNet / Cunningham project needs your help!! The Cunningham project is trying to complete the factorization of 2^n-1 and 2^n+1 where n < 1200. To do this they need to find as many "small" factors as possible using ECM. Computers of all speeds are welcome, but this project is ideal for slower computers because primality tests on large Mersenne numbers can take months to complete. Visit 2^n-1 and 2^n+1 for current ECM status. Visit the forums for help setting up prime95 to run ECM curves.

Other Recent News M971 factored.On September 13, 2004 David Symcox cracked the smallest Mersenne number with no known factor - finding a 53-digit factor for M971.

41st Mersenne Prime found. On May 15, 2004, Josh Findley discovers 224,036,583-1 is prime.

M6972593 is the 38th Mersenne prime. GIMPS has finished testing and double-checking all Mersenne numbers below M6972593. This proves there are no smaller undiscovered Mersenne primes.

GIMPS forums. Here you can chat with fellow GIMPS members, get help with installation questions, learn more about how GIMPS works, etc.

Make Math History!! You could discover one of the most coveted finds in all of Mathematics - a new Mersenne prime number. We've found nine already. Join in on this fun, yet serious research project. All you need is a personal computer, patience, and a lot of luck.

In addition to the joy of making a mathematical discovery, you might win some cash. The Electronic Frontier Foundation is offering a $100,000 award to the first person or group to discover a ten million digit prime number! See how GIMPS will distribute this award if we are lucky enough to find the winning ten million digit prime.

What are Mersenne primes and why do we search for them? Prime numbers have long fascinated amateur and professional mathematicians. An integer greater than one is called a prime number if its only divisors are one and itself. The first prime numbers are 2, 3, 5, 7, 11, etc. For example, the number 10 is not prime because it is divisible by 2 and 5. A Mersenne prime is a prime of the form 2P-1. The first Mersenne primes are 3, 7, 31, 127 (corresponding to P = 2, 3, 5, 7). There are only 43 known Mersenne primes.

GIMPS, the Great Internet Mersenne Prime Search, was formed in January 1996 to discover new world-record-size Mersenne primes. GIMPS harnesses the power of thousands of small computers like yours to search for these "needles in a haystack".

Most GIMPS members join the search for the thrill of possibly discovering a record-setting, rare, and historic new Mersenne prime. Of course, there are many other reasons.

Site Map The How it Works page tells you what hardware you need and how the program runs.

The Download page lets you download the free software.

The FAQ page answers some frequently asked questions.

The benchmarks page compares the programs speed on many different CPU types.

The Prizes page tells you how GIMPS will divide any prize money.

The Status page tells you how the search is progressing.

The Top Producers page ranks participants by CPU time contributed.

The PrimeNet page gives statistics maintained by the server.

The History page gives a brief history of the project.

The Math page describes the math and algorithms GIMPS uses.

The Source code page lets you download the source code and gives UNIX users a pointer to code they can use.

The Mailing list page lets you subscribe to a mailing list that discusses Mersenne numbers.

The Manual testing page lets you pick exponents to test if you cannot get the PrimeNet server to work.

The Credits page lists many of the people that have helped GIMPS over the years.

The Links page gives you pointers to several other web sites.

The Other projects page gives you pointers to other distributed computing projects.

Last updated: December 24, 2005

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Getting started: Main page | How it works | Download | FAQ | Benchmarks | Prizes

Learning more: History | The math | Source code | Mailing list

Project status: Status | Top producers | PrimeNet

Miscellaneous: Manual testing | Credits | Links | Feedback | Other projects