Marin Mersenne 2^P-1
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Great Internet Mersenne Prime Search
GIMPS
Finding World Record Primes Since 1996
Today's Numbers
Teams1,506
Users240,501
CPUs2,337,707
TFLOP/s863.023
GHz-Days431,512

Welcome to GIMPS, the Great Internet Mersenne Prime Search

To join GIMPS,

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Previous Day Stats
First Prime Tests348
Verified Prime Tests549
Newly Factored360

All exponents below 58 069 853 have been tested and verified.
All exponents below 105 267 119 have been tested at least once.

All tests smaller than the 48th Mersenne Prime, M(57885161), have been verified

M(57885161) was discovered eight and half years ago. Now, thanks to the largely unheralded and dedicated efforts of thousands of GIMPS volunteers, every smaller Mersenne number has been successfully double-checked. Thus, M(57885161) officially becomes the 48th Mersenne prime. This is a significant milestone for the GIMPS project.

First-time Lucas-Lehmer Testing Ends

One year ago, first-time PRP primality testing with proofs was introduced. It has been a huge success, saving GIMPS tens of thousands future double-checks. Going forward, the server will no longer make available exponents for first time Lucas-Lehmer tests. Users that have not yet upgraded to prime95 version 30.3 or gpuowl for GPUs should do so. Failure to upgrade will result in necessary double-check work. GIMPS has a multi-year backlog of double-checks to work through. There is even a chance that a new Mersenne prime is hidden in all those double-checks.

The server will continue to accept Lucas-Lehmer results. There is no need to worry about any LL tests that are currently underway.

BIG Changes Are Here! Prime95 version 30.3 released.

For almost 25 years, GIMPS has looked for new Mersenne primes by running a primality test on one computer and later running the exact same primality test on another computer to guard against hardware errors having corrupted the first primality test.

A breakthrough by Krzysztof Pietrzak makes it possible to eliminate the second primality test! The first primality test produces a proof file that can be securely verified with less than 0.5% of the work required to re-run the primality test. This breakthrough will nearly double GIMPS' throughput in the long run.

Version 30.3 is now available with PRP proofs. While not a required upgrade, at some point in the future only users running version 30.3 with PRP proofs will be assigned first-time primality tests. Should you run into any problems, support is available at this thread at Mersenne Forum.

Many thanks to Mihai Preda for discovering the paper on the breakthrough and realizing its importance to the GIMPS project. Also, thanks go to Pavel Atnashev for important ideas on adapting the discovery for use by GIMPS.

GIMPS Shirts For Sale!

shirt

Show your love of math and prime numbers with a GIMPS shirt! Friends and family will surely be impressed. Viliam Furik has taken the initiative to create, manufacture, and sell GIMPS polo and T-shirts. Viliam will not profit from the sale of the shirts. Any "loose change" from price rounding will be donated to GIMPS. Shirts are sold for the price of the shirt itself and embroidering. Custom text can be added upon request.

Price is expected to be about $9 for a T-shirt and $13 for a polo, plus shipping. Shipping ranges from $6.50 to $10 to Europe, USA, Argentina, Brasil, Canada, China, Egypt, Hong Kong, India, Israel, Japan, S. Korea, Mexico, Russia, Thailand, Turkey, and U.S. territories.

The pre-order/interest form is here.

The latest information on expected order date (we get a cheaper price if we order a batch of 50 or more), shirt sizing, etc. can be found here at MersenneForum. You can also ask questions of Viliam on the forum.

BOINC users with GPUs can now participate

SRBase has created a BOINC project to hand out trial factoring assignments on large Mersenne numbers. These are very quick work units. To get the most of the BOINC client without any issues, a FAQ at the SRBASE forum is available.

Note that there’s no way to individually credit SRBase users in GIMPS trial factoring stats. All work is credited to GIMPS user SRBase.

51st Known Mersenne Prime Found!

December 21, 2018 — The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 282,589,933-1, having 24,862,048 digits. A computer volunteered by Patrick Laroche from Ocala, Florida made the find on December 7, 2018. The new prime number, also known as M82589933, is calculated by multiplying together 82,589,933 twos and then subtracting one. It is more than one and a half million digits larger than the previous record prime number.

GIMPS has been on amazing lucky streak finding triple the expected number of new Mersenne primes -- a dozen in the last fifteen years. This prime was even luckier for Patrick Laroche, striking pay dirt on just his fourth try. For years, Patrick had used GIMPS software as a free "stress test" for his computer builds. Less than four months ago he started prime hunting on his media server to give back to the project. By way of comparison, some GIMPS participants have searched for more than 20 years with tens of thousands of attempts but no success. This proves that, with luck, anyone can find the next new Mersenne prime.

The new prime is only the 51st known Mersenne prime ever discovered. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. GIMPS, founded in 1996, has discovered the last 17 Mersenne primes. Volunteers download a free program to search for these primes, with a cash award offered to anyone lucky enough to find a new prime. Prof. Chris Caldwell maintains an authoritative web site on the largest known primes, and has an excellent history of Mersenne primes.

Patrick is one of thousands of volunteers using free GIMPS software available at www.mersenne.org/download/. Credit for this prime goes not only to Patrick Laroche for running the Prime95 software, Woltman for writing the software, Blosser for keeping the Primenet server running smoothly, and the thousands of GIMPS volunteers that sifted through millions of non-prime candidates.  In recognition of all the above people, official credit for this discovery goes to "P. Laroche, G. Woltman, A. Blosser, et al."

You can read a little more in the press release.

More News and Discussions

GIMPS forumsHere 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 fifteen 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 could win a (USD) $3,000 cash GIMPS Research Discovery Award for each Mersenne prime discovered, and the Electronic Frontier Foundation is offering a $150,000 award to the first person or group to discover a 100 million digit prime number! See how GIMPS will distribute this award if we are lucky enough to find the winning 100 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 51 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.


Last Updated October 6, 2021