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Largest Known Prime, 48th Known Mersenne Prime Found!!
On January 25th, 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
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
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.
Prime95 version 27 released! Faster on Intel's newer CPUs!
May 15, 2012. You may download version 27 now. The FFT assembly code
has been rewritten for better speed on Intel's newer CPUs supporting AVX instructions. Sandy Bridge and Ivy Bridge
CPUs (Core i3/i5/i7-2xxx and 3xxx models) should see a huge performance increase.
To upgrade, simply exit
Prime95, download the new version, and unzip the new version replacing the old version.
GIMPS now accepting donations
GIMPS is now accepting donations to help fund server upgrades and future Mersenne Prime prize awards.
Donations are tax-deductible in the U.S.
M(24036583) proven to be 41st Mersenne Prime
December 1, 2011. More than 6 years after discovering M(24036583), GIMPS finished double-checking every smaller
Mersenne number. Since no primes were found, the "41st known Mersenne prime" can now
be simply called the "41st Mersenne prime". Congratulations and thanks to all the GIMPS members
that perform this less glamorous double-checking work.
October 14, 2009:
GIMPS Wins EFF $100,000
Cooperative Computing Award!
Could YOU be the next person to discover a new Mersenne
prime and win a cash research award?
The Electronic Frontier Foundation awarded
GIMPS the $100,000
Cooperative Computing Award for the August 23rd, 2008 discovery of the 45th known Mersenne prime
a mammoth 12,978,189 digit number,
found on a University of California Los Angeles (UCLA) computer in the GIMPS
PrimeNet network, after GIMPS
met every requirement
$100,000 award for discovery of
the first 10 million digit prime number.
As promised, GIMPS gave $50,000 of the EFF award to the UCLA Department of
Mathematics, where Edson Smith was responsible for installing and maintaining the GIMPS software on
their computers. Another $25,000 has been donated to a math-related charity
selected by GIMPS founder George Woltman. The remaining $25,000 has been
paid in GIMPS Mersenne
Prime Research Discovery Awards to Odd Magnar Strindmo for his discovery of
M47, Hans-Michael Elvenich for M46, the University of Central Missouri (M44 and
M43), Dr. Martin Nowak (M42), Josh Findley (M41), Michael Shafer and his
selected charity (M40) and Michael Cameron (M39).
Chris Caldwell maintains an excellent web site on prime numbers.
See his page on Mersenne Primes and their history.
GIMPS has found 13 of the 47 Mersenne primes ever found during its 13 year history.
||Recently joined GIMPS:
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 fourteen 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
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 46 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 February 5, 2013