 |
|
DAILY NEWS AND INFORMATION FOR THE GLOBAL GRID COMMUNITY /
|
Special Features:
GIMPS PROJECT DISCOVERS NEW LARGEST KNOWN PRIME NUMBER
Josh Findley, a volunteer in the Mersenne.org research project called the
Great Internet Mersenne Prime Search (GIMPS), has discovered the largest known
prime number. Findley used his home PC and free software by George Woltman and
Scott Kurowski as part of an international Grid of 240,000 networked computers
in virtually every time zone of the world.
The new number, expressed as 2 to the 24,036,583th power minus 1, has
7,235,733 decimal digits and was discovered May 15. It is nearly a million
digits larger than the previous largest known prime number, and belongs to a
special class of rare prime numbers called Mersenne primes. The discovery
marks only the 41st known Mersenne prime, named after Marin Mersenne, a 17th
century French monk who first studied the rare numbers 300 years ago. Mersenne
primes are most relevant to number theory, but most participants join GIMPS
simply for the fun of having a role in real research -- and the chance of
finding a new Mersenne prime.
GIMPS is closing in on the $100,000 Electronic Frontier Foundation award for
the first 10-million-digit prime. The new prime is 72 percent of the size
needed. However, "an award-winning prime could be mere weeks or as much as few
years away -- that's the fun of math discoveries," said GIMPS founder George
Woltman.
The GIMPS participant who discovers the prime will receive $50,000. Charity
will get $25,000. The rest will be used primarily to fund more prime
discoveries. In May 2000, a previous participant won the foundation's $50,000
award for discovering the first million-digit prime.
Findley, a consultant to the National Oceanic and Atmospheric Administration
(NOAA) in La Jolla, Calif., described the find. "I'm still surprised at the
discovery. Even after five years running GIMPS on my computers, I didn't
expect to find a new Mersenne prime." He used a 2.4 GHz Pentium 4 Windows XP
PC running for 14 days to prove the number prime. "I joined GIMPS because it
seemed the logical choice for using my spare CPU cycles."
Now in its eighth year, GIMPS has accomplished what no other distributed
computing project has: seven consecutive successes. "Great teamwork has paid
off for us again," said Woltman. "In addition to congratulating Josh Findley,
we wish to thank all 75,000 volunteer home users, students, schools,
universities and businesses from around the world that contributed to this
discovery. Joining GIMPS is a great way to learn about math through
participation -- and you might find a new Mersenne prime, like Josh."
"PrimeNet organizes a vast computing resource for GIMPS. It's humbling to see
so many people of varied lands, ages and vocations volunteering for this fun
and amazing project," said Entropia founder Scott Kurowski. Kurowski developed
the PrimeNet system that runs GIMPS. PrimeNet pulls together hundreds of
thousands of computers in parallel to create a virtual supercomputer running
at 14 trillion calculations per second, or "teraflops." This enabled GIMPS to
find the prime in just six months instead of the 2,500 years a single PC would
have required.
The new prime was independently verified by Tony Reix of Grenoble, France,
using half of a Bull NovaScale 5000 HPC running Linux on 16 Itanium II 1.3 GHz
CPUs for five days using the Glucas program by Guillermo Ballester Valor of
Granada, Spain, and by Jeff Gilchrist of Elytra Enterprises Inc in Ottawa,
Canada, using 11 days of time on a HP rx5670 quad Itanium II 1.5 GHz CPU
server at SHARCNET. The discovery is the seventh record prime found by the
GIMPS project. In recognition of every GIMPS contributor's effort, credit for
this new discovery will go to "Findley, Woltman, Kurowski, et al."
"There are more primes out there," invited Woltman, "and anyone with an
Internet-connected computer can participate."
All the necessary software can be downloaded for free at
www.mersenne.org . The calculations work by using spare background time
that would otherwise be wasted. Please get permission to install the software
on computers you do not own.
The mathematical algorithm Woltman uses for GIMPS, called the IBDWT
(irrational-base discrete weighted transform), was discovered by Apple
Distinguished Scientist Richard Crandall, director of the Center for Advanced
Computation at Reed College (Portland, Ore.). A framed or unframed poster (and
optional magnifying glass) displaying the multi-million-digit prime number is
available from Perfectly Scientific Inc. The IBDWT and related algorithms are
available in the book, "Prime Numbers: A Computational Perspective," by R.
Crandall and C. Pomerance.
Findley is an independent IT consultant living in Issaquah, Wash. He joined
GIMPS in June 1999. Woltman is a retired computer programmer living in
Orlando, Fla. A life-long number theory enthusiast, he founded GIMPS in 1996.
Kurowski is a software technologist and entrepreneur in San Diego. A GIMPS
member since 1996, he built PrimeNet and founded Entropia Inc in 1997.
More Information on Mersenne Primes
Previous GIMPS Mersenne prime discoveries were made by members in various
countries. In November 2003, Michael Shafer discovered the previous largest
known prime number in the United States. In November 2001, Michael Cameron
discovered the the 39th Mersenne prime in Canada. In June 1999, Nayan
Hajratwala discovered the 38th Mersenne prime in the United States. In January
1998, Roland Clarkson discovered the 37th Mersenne prime in the United States.
Gordon Spence discovered the 36th Mersenne prime in August, 1997, in the
United Kingdom. Joel Armengaud discovered the 35th Mersenne prime in November
1996 in France.
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, etc.
There are only 41 known Mersenne primes.
Mersenne primes have been central to number theory since they were first
discussed by Euclid in 350 B.C. The man whose name they now bear, the French
monk Marin Mersenne, made a famous conjecture on which values of p would yield
a prime. It took 300 years and several important discoveries in mathematics to
settle his conjecture.
There is a unique history to the arithmetic algorithms underlying the GIMPS
project. The programs that found the recent big Mersenne finds are based on a
special algorithm. In the early 1990's, Crandall discovered ways to double the
speed of what are called convolutions -- essentially big multiplication
operations. The method is applicable not only to prime searching but other
aspects of computation. During that work he also patented the Fast Elliptic
Encryption system, now owned by Apple Computer, which uses Mersenne primes to
quickly encrypt and decrypt messages. George Woltman implemented Crandall's
algorithm in machine language, thereby producing a prime-search program of
unprecedented efficiency, and that work led to the successful GIMPS project.
Several hundred school teachers elementary through high-school grades have
used GIMPS to get their students excited about mathematics. Students who run
the free software are contributing to mathematical research.
Historically, searching for Mersenne primes has been used as a test for
computer hardware. The free GIMPS program used by Findley has identified
hidden hardware problems in many PCs.
|