Note: This is no longer the largest known prime
The
largest known
prime number may be found in
chongo's table of
Mersenne Prime
Digits and Names.
CRUNCHING NUMBERS
RESEARCHERS MAKE PRIME MATH DISCOVERY
Published: Tuesday, September 3, 1996
Section: Front
Page: 1A
BY DAN GILLMOR, Mercury News Computing Editor
When the British mountaineer George Leigh Mallory was asked why he wanted
to scale Mount Everest, he replied: ''Because it's there.''
A related urge sparks computer scientists at Silicon Graphics Inc.'s Cray
Research unit, who will announce today that they've discovered the world's
largestknown prime number  and a special kind of prime number at that. This
one is 378,632 digits long, roughly 120 singlespaced typewritten pages  and
''a rare jewel,'' said codiscoverer Paul Gage.
But the way they found it, using sophisticated programming on highpowered
supercomputers, goes well beyond mathematical mountain climbing. The
techniques help create and test computer systems that in turn help solve
realworld problems such as cryptography, improving weather forecasts and
designing safer cars, said David Slowinski, the other codiscoverer of the
latest record number.
Using a Cray T94 supercomputer, Slowinski and Gage found what is currently
the biggest example of a Mersenne prime number, named after a 17thcentury
French monk, Father Marin Mersenne, who had a thing for numbers. A prime
number is an integer greater than zero whose divisors are only itself and 1.
(The number 2 is prime because it can only be divided evenly by 1 and 2, for
example). Mersenne numbers are primes that take the form 2 to some power,
minus 1  in other words, 2 multiplied by itself a certain number of times
with 1 subtracted from the result.
The smallest Mersenne prime is 3, or 2 to the 2nd power (2x2=4) minus 1.
The next largest ''regular'' prime number is 5, and the next largest Mersenne
prime is 7, or 2 to the 3rd power (2x2x2=8) minus 1. Two to the 4th power (16)
minus one equals 15, not a prime number since it can be divided by 1, itself,
3 and 5. But 2 to the 5th power (32) minus 1  31  is a Mersenne prime.
Not their first
The latest discovery  only the 34th known Mersenne prime  is 2 to the
1,257,787th power (2 multiplied by itself 1,257,787 times) minus 1. The
previous largestknown Mersenne prime, 2 to the 859,433rd power minus one, was
discovered by Slowinski and Gage in 1994. Slowinski has been a Mersenne
discoverer or codiscoverer seven times. This is Gage's third codiscovery.
One elegant oddity about Mersenne primes is a mathematical connection to
other intriguing integers. For every Mersenne prime, there's a corresponding
(but larger) ''perfect number,'' a class of integers that fascinates
mathematicians. Perfect numbers are equal to the sum of all of their positive
divisors, except themselves; for example, 6 is a perfect number (1+2+3=6).
Back to Euclid
Perfect numbers and what later came to be called Mersenne primes date
actually back to the legendary Greek mathematician, Euclid, said Carl
Pomerance, professor of mathematics at the University of Georgia in Athens. It
was Euclid who noticed the connection. Later, Mersenne spent years looking for
the integers that now bear his name.
''In modern days,'' Pomerance said, ''they've become a benchmark for
computers.''
Silicon Graphics is a hotbed of primenumber research. People who work at
SGI or its subsidiaries have been involved in the discovery of the last 10
recordsetting primes, according to Landon Curt Noll, a cryptographer and
member of Information Security Infrastructure Team at the Mountain Viewbased
company. Noll has held or shared the Mersenne record twice. Slowinski works at
Cray's Chippewa Falls, Wis., manufacturing plant. Gage is based at Cray's
headquarters in Eagan, Minn.
One purpose of the Mersenne testing is to put new Cray machines through the
paces before sending them to customers. Slowinski and Gage have ''a lot of
fun, but they really are doing the company a service,'' said Cray spokeswoman
Mardi Larson.
The computer scientists' latest Mersenne discovery occurred last spring. As
is customary, they asked independent researchers to doublecheck their work
before making it public.
Competitor checks it
One tester was George Woltman, a programmer in Florida who has been hunting
for Mersenne primes from a different direction. He and about 400 volunteers
around the world have been searching systematically using PCs powered by Intel
Corp. Pentium processors. They need as many machines as they can get; just one
Cray processor checked the latest Mersenne prime in about six hours, but a
90megahertz Pentium took more than 60 hours.
Woltman said he was about 90 percent of the way through the very number
that Slowinski and Gage found when they told him about their discovery and
asked him to doublecheck it.
''It hurt for a few days, but I got over it,'' he said. ''It doesn't
diminish my enthusiasm. We'll never run out of exponents to check.''
For more information on the latest Mersenne prime, point
your World Wide Web browser to
http://www.isthe.com/chongo/tech/math/prime/prime_press.html.
For more information on George Woltman's
project to use PCs in the search, point your browser to
http://www.mersenne.org.
And if you really want to see what the largestknown prime number
looks like, point your browser to
http://www.isthe.com/chongo/tech/math/prime/m1257787.html.
Copyright 1996, The San Jose Mercury News. Unauthorized reproduction
prohibited.
The San Jose Mercury News archives are stored on a SAVE (tm) newspaper library system from MediaStream, Inc., a KnightRidder Inc. company.
Note: This is no longer the largest known prime
The
largest known
prime number may be found in
chongo's table of
Mersenne Prime
Digits and Names.
