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Great Internet Mersenne Prime Search
GIMPS
Finding World Record Primes Since 1996
Today's Numbers
Teams1,226
Users193,547
CPUs1,701,816
TFLOP/s348.220
GHz-Days174,110

Welcome to GIMPS, the Great Internet Mersenne Prime Search

To join GIMPS,

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Previous Day Stats
First Time LL Tests334
Verified LL Tests288
Newly Factored477

All exponents below 43 920 223 have been tested and verified.
All exponents below 78 413 429 have been tested at least once.

Prime95 version 29.4 - Recommended update

Version 29.4 (build 7 or 8) is the latest version available for download. The most significant change with version 29 builds are the changes to "probable prime" (PRP) tests. An error checking method called Gerbicz (named for Robert Gerbicz who proposed the method) can help ensure an error-free PRP test and may eventually be a way to eliminate the need for double-checks.

Additionally, Jacobi error checks have been added to LL tests to help identify errors and can roll back a test to the "last known good" save file if an error was detected. This should help reduce the error rate of completed tests as more users update to the latest version.

Other improvements include fast, multi-threaded trial factoring for multi-core CPUs, plus AVX512 support for trial factoring. A new benchmarking method will run periodic benchmarks of various FFT sizes to determine which settings work the best for your individual system.

You can view the full list of changes in the version history file here.

All tests smaller than M(43112609) have been verified, officially making it the 47th Mersenne Prime

April 8, 2018 — Nearly 9 years ago in August 2008, M(43112609) was discovered, and now GIMPS has finished verification testing on every smaller Mersenne number. With no smaller primes found, M(43112609) is officially the 47th Mersenne prime.

At the time of the discovery, M(43112609) was actually the 45th known Mersenne prime because M(37156667) wasn't discovered until 2 weeks later, and M(42643801) was found nearly a year later in June of 2009! The last time a Mersenne prime was discovered out of order was in 1988 when M(110503) was found over 4 years after M(132049), and in 1961 M(4423) was discovered mere seconds before M(4253) because of the order in which the printout was read.

This highlights the importance of waiting until all smaller exponents have been tested and verified before we can say definitively where any Mersenne prime is ranked. Due to the distributed nature of the project as a whole, numbers are not always tested in order and a smaller Mersenne prime may yet be found. For that reason, thanks to all the GIMPS members that contributed their resources towards achieving this milestone. Join now to help GIMPS press onward with verification tests to prove M(57885161) is the 48th Mersenne prime!

All tests smaller than M(42643801) have been verified, officially making it the 46th Mersenne Prime

February 22, 2018 — Nearly 9 years ago in June 2009, M(42643801) was discovered, and now GIMPS has finished verification testing on every smaller Mersenne number. With no smaller primes found, M(42643801) is officially the 46th Mersenne prime. Thanks to all the GIMPS members that contributed their resources towards achieving this milestone. Join now to help GIMPS press onward with verification tests to prove M(43112609) is the 47th Mersenne prime.

Verification tests are an important part of the GIMPS project. Errors can occur during a test of smaller numbers, invalidating the end result. Only by doing a double-check with matching results are we able to say for sure that a Mersenne number is composite. Until all numbers below a Mersenne prime have been verified, we don't know for sure if it's the 46th known Mersenne prime or if there might be a smaller one that we missed due to a machine error, so we at GIMPS celebrate these important verification milestones.

50th Known Mersenne Prime Found!

January 3, 2018 — Persistence pays off. Jonathan Pace, a GIMPS volunteer for over 14 years, discovered the 50th known Mersenne prime, 277,232,917-1 on December 26, 2017. The prime number is calculated by multiplying together 77,232,917 twos, and then subtracting one. It weighs in at 23,249,425 digits, becoming the largest prime number known to mankind. It bests the previous record prime, also discovered by GIMPS, by 910,807 digits.

Just how big is a 23,249,425 digit number? It's huge!! Big enough to fill an entire shelf of books totalling 9,000 pages! If every second you were to write five digits to an inch then 54 days later you'd have a number stretching over 73 miles (118 km) -- almost 3 miles (5 km) longer than the previous record prime.

Jonathan Pace is a 51 year old Electrical Engineer living in Germantown Tennessee. He is a long-time math enthusiast now working at FedEx and active in community charities. As SysAdmin for his charities, he runs Prime95 on all PCs and servers because GIMPS emails him if one doesn't check in, which is helpful for monitoring these remote computers from home or work. The PC that found the new prime took six days of intense computation on a quad-core Intel i5-6600 CPU to prove the number prime.

To be thorough, the prime number was independently verified with four different programs running on various hardware configurations.

In recognition of the individual discoverer, the software authors, the GIMPS project leaders, and every GIMPS participant's contribution, credit for the new prime goes to "Jonathan Pace, George Woltman, Scott Kurowski, Aaron Blosser, et al.".

Could you be the next lucky volunteer to discover a brand new Mersenne Prime? You'll need a reasonably modern PC and the free software on the download page.

You can read a little more in the press release.

Largest Known Prime, 49th Known Mersenne Prime Found!!

January 7, 2016 — GIMPS celebrated its 20th anniversary with the discovery of the largest known prime number, 274,207,281-1. Curtis Cooper, one of many thousands of GIMPS volunteers, used one of his university's computers to make the find. The prime number, also known as M74207281, is calculated by multiplying together 74,207,281 twos then subtracting one. It has 22,338,618 digits -- almost 5 million digits longer than the previous record prime number

While prime numbers are important for cryptography, this prime is too large to currently be of practical value. However, the search itself does have several practical benefits. Historically, searching for Mersenne primes has been used as a test for computer hardware. Earlier this month, GIMPS' prime95 software and members of a German computing community uncovered a flaw in Intel's latest Skylake CPUs. Prime95 has also discovered hardware problems in many individual's PCs.

To prove there were no errors in the prime discovery process, the prime was independently verified using both different programs and different hardware. Andreas Hoglund and David Stanfill each verified the prime using the CUDALucas software running on NVidia Titan GPUs. David Stanfill also verified using ClLucas on an AMD Fury GPU. Finally, Serge Batalov ran Ernst Mayer's MLucas software on a 18-core server to verify the prime.

Dr. Cooper is a professor at the University of Central Missouri. This is the fourth record prime for Dr. Cooper and his university. Their first record prime was discovered in 2005, eclipsed by their second record in 2006. Dr. Cooper lost the record in 2008, but reclaimed it in 2013, and improved the record with this new prime. The primality proof took a month of computing on a PC with an Intel I7-4790 CPU.  Dr. Cooper and the University of Central Missouri is the largest contributor of CPU time to the GIMPS project. The discovery is eligible for a $3,000 GIMPS research discovery award.

While Dr. Cooper's computer found the record prime, the discovery would not have been possible without all the GIMPS volunteers that sifted through numerous non-prime candidates. GIMPS founder George Woltman, PrimeNet creator Scott Kurowski, Primenet administrator Aaron Blosser, thank and congratulate all the GIMPS members that made this discovery possible. To recognize all those that contributed to this discovery, official credit goes to Cooper, Woltman, Kurowski, Blosser, et al.

The new prime number is a member of a special class of extremely rare prime numbers known as Mersenne primes. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. There are only 49 known Mersenne primes. GIMPS, founded in 1996, has discovered the last 15 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 as well an excellent history of Mersenne primes.

Interestingly, Dr. Cooper's computer reported the prime to the server on September 17, 2015. However, a bug prevented the email notification from being sent. The new prime remained unnoticed until routine database maintenance took place months later. The official discovery date is the day a human took note of the result. This is in keeping with tradition as M4253 is considered never to have been the largest known prime number because Alexander Hurwitz in 1961 read his computer printout backwards and saw M4423 was prime seconds before seeing that M4253 was also prime.

You can learn a little more in the short press release or watch the standupmaths interview with Curtis Cooper regarding his discovery:

New Assignment and Recycling Rules

February 2014 — Since 2008, GIMPS has given users one year to complete assignments. This rule has not been enforced. This has held up completing milestones as some assignments did not complete even after several years.

During February 2014, new assignment and recycling policies were put in place to help GIMPS make steady progress on milestones by detecting assignments that are proceeding extremely slowly or not at all.

This affects users in two ways:

Users testing 100 million digit numbers are not affected by these new rules. Assignments made prior to March 1, 2014 will be given a year, as promised, to complete (plus a grace period if the assignment is close to complete).

Largest Known Prime, 48th Known Mersenne Prime Found!!

January 25th, 2013 — Prolific GIMPS contributor Dr. Curtis Cooper discovered the 48th known Mersenne prime, 257,885,161-1, a 17,425,170 digit number. This find shatters the previous record prime number of 12,978,189 digits, also a GIMPS prime, discovered over 4 years ago. The discovery is eligible for a $3,000 GIMPS research discovery award.

Dr. Cooper is a professor at the University of Central Missouri. This is the third record prime for Dr. Cooper and his University. Their first record prime was discovered in 2005, eclipsed by their second record in 2006. Computers at UCLA broke that record in 2008. UCLA held the record until Dr. Cooper and the University of Central Missouri reclaimed the world record with this discovery.

While Dr. Cooper's computer found the record prime, the discovery would not have been possible without all the GIMPS volunteers that sifted through numerous non-prime candidates. GIMPS founder George Woltman and PrimeNet creator Scott Kurowski thank and congratulate all the GIMPS members that made this discovery possible.

Mersenne primes are extremely rare, only 48 are known. GIMPS, founded in 1996, has discovered the last 14 Mersenne primes. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. Chris Caldwell maintains an authoritative web site on the history of Mersenne primes as well as the largest known primes.

The primality proof took 39 days of non-stop computing on one of the University of Central Missouri's PCs. To establish there were no errors during the proof, the new prime was independently verified using different programs running on different hardware. Jerry Hallett verified the prime using CUDALucas running on a NVidia GPU in 3.6 days. Dr. Jeff Gilchrist verified the find using the standard GIMPS software on an Intel i7 CPU in 4.5 days. Finally, Serge Batalov ran Ernst Mayer's MLucas software on a 32-core server in 6 days (resource donated by Novartis IT group) to verify the new prime.

You can read a little more in the short press release.

GIMPS now accepting donations

GIMPS is now accepting donations to help fund server co-location fees and future Mersenne Prime prize awards. Donations are tax-deductible in the U.S.

Older News

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.

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 49 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 January 19, 2016