Great Internet Mersenne Prime Search GIMPS Finding World Record Primes Since 1996

Today's Numbers

Teams

1,134

Users

178,823

CPUs

1,567,484

TFLOP/s

306.500

GHz-Days

153,250

Welcome to GIMPS, the Great Internet Mersenne Prime Search

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M(37156667) proven to be 45th Mersenne Prime

September 2, 2016 — In 2008, M(37156667) was discovered, and after 8 years GIMPS has finished checking and
double-checking every smaller Mersenne number. With no new, smaller primes found,
M(37156667) is officially the "45th Mersenne
prime". Thanks to all the GIMPS members that contributed their resources towards achieving this milestone.
Join now to help GIMPS press onward to proving M(42643801) is the 46th Mersenne prime.

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, 2^{74,207,281}-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:

M(32582657) proven to be 44th Mersenne Prime

November 8, 2014 — In 2006, M(32582657) was discovered, and after 8 years GIMPS has finished checking and
double-checking every smaller Mersenne number. With no new, smaller primes found,
M(32582657) is officially the "44th Mersenne
prime". Congratulations and thanks to all the
GIMPS members that contributed their resources towards this milestone.

Prime95 version 28 released! Faster on Intel's latest CPUs!

June 1, 2014 — Version 28 is now available for download. The FFT assembly code
has been optimized to use Intel's fused multiply-add instructions on Intel's Haswell CPUs (Core i3/i5/i7-4xxx models).
Haswell users should see a decent performance increase. Sandy Bridge and Ivy Bridge users may also see a small
speed boost due to some memory bandwidth optimizations.
To upgrade, simply exit Prime95, download the new version, and unzip the new version replacing the old version.

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:

When they occasionally become available, if you want to test the
smallest exponents you'll need to sign up on the
assignment rules page and be aware of the shorter timeline for returning
results.

Your computers that are proven producers will have 8 or 9 months to
complete assignments. Your slower computers and computers with a limited track record
will still have a full year to complete their assignments.

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).

M(30402457) proven to be 43rd Mersenne Prime

February 23, 2014 — More than 8 years after discovering M(30402457), GIMPS has finished checking and
double-checking every smaller Mersenne number. With no new primes found that are smaller
than M(30402457), the "43rd known Mersenne
prime" can now be called the "43rd Mersenne prime". Congratulations and thanks to all the
GIMPS members that perform this somewhat less glamorous double-checking work.

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

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.

M(25964951) proven to be 42nd Mersenne Prime

December 20, 2012 — One year after proving the 41st Mersenne prime, GIMPS
finished double-checking every smaller Mersenne number than M(25964951) -- proving that this prime is indeed the 42nd Mersenne
prime. There are 47 known Mersenne primes. Mersenne primes are sometimes
discovered out-of-order. It is not yet known if there is an undiscovered Mersenne prime between
M(25964951) and the next largest known Mersenne prime,
M(30402457). Here is a list of all GIMPS milestones and our progress toward future ones. Congratulations and
thanks to all the GIMPS members that contributed to this important double-checking
work.

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 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 fifteen already. Join in on this fun, yet serious
research project. All you need is a personal computer, patience, and a lot of
luck.

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 2^{P}-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.