Steve Conway, 612/683-7133



LARGEST KNOWN PRIME NUMBER DISCOVERED ON CRAY

RESEARCH SUPERCOMPUTER



EAGAN, Minn., Jan. 10, 1994 -- Computer scientists at Cray

Research, Inc. have discovered the largest-known prime

number while conducting tests on a CRAY C90 series

supercomputer.



The new prime number has 258,716 digits.  Printed in

newspaper-sized type, the number would fill approximately 8

newspaper pages.



In mathematical notation, the new prime number is expressed

as 2^859433-1, which denotes two, multiplied by itself

859,433 times, minus one.  Numbers expressed in this form are

called "Mersenne" prime numbers after Father Marin Mersenne,

a 17th century French monk who spent years searching for

prime numbers of this type.



The largest Mersenne prime known previously was discovered

in February 1992 at AEA Technology's Harwell Laboratory in

England by computer scientists who were also conducting a

test of a Cray Research supercomputer.  It had 227,832 digits. 

Six of the last seven Mersenne primes were discovered on Cray

Research supercomputers.



Prime numbers can be divided evenly only by themselves and

one.  Examples include 2, 3, 5, 7, 11 and so on.  The Greek

mathematician Euclid proved that there are an infinite number

of prime numbers.  But these numbers do not occur in a regular

sequence and there is no formula for generating them. 

Therefore, the discovery of new primes requires randomly

generating and testing millions of numbers. 



"Finding these special numbers is a true 'needle-in-a-haystack'

exercise, but we improve our odds by using a tremendously

fast computer and a clever program," said David Slowinski, a

Cray Research computer scientist.  Slowinski and fellow Cray

Research computer scientist Paul Gage developed the program

that found the new prime number.  Mathematician Richard

Crandall, Ph.D., independently verified that the number

Slowinski and Gage found is prime and will note the discovery

in a textbook to be published shortly.



Prime numbers have applications in cryptography and computer

systems security.  Huge prime numbers like those discovered

most recently are principally mathematical curiosities, but

the process of searching for prime numbers does have several

practical benefits.



For instance, the "prime finder" program developed by

Slowinski and Gage is used by Cray Research as a quality

assurance test on all new supercomputer systems.  A core

element of this program is a routine that involves squaring a

number repeatedly.  As this process continues, it eventually

involves multiplying immense numbers -- numbers of hundreds

of thousands of digits -- by themselves.



"This acts as a real 'torture test' for a computer," said

Slowinski.  "The prime finder program rigorously tests all

elements of a system -- from the logic of the processors, to

the memory, the compiler and the operating and multitasking

systems.  For high performance systems with multiple

processors, this is an excellent test of the system's ability to

keep track of where all the data is." Slowinski said the recent

CRAY C90 test in which the new prime number was discovered

would run for over 7 hours on one central processing unit of

the system.  "If a machine can complete this exhaustive

run-through, we can be confident everything is working as it

should," said Slowinski.



In addition, Slowinski said, techniques used to speed up the

performance of the prime finder can also be used to enhance

the performance of programs customers use on real-world

problems such as forecasting the weather and searching for

oil.  "Through our work on the prime finder program, we learn

new techniques for speeding up certain kinds of mathematical

operations.  These operations are often key elements of the

most computation-intensive portions of software 

programs our customers run on their systems," said Slowinski.



Slowinski compared running the prime finder on

supercomputers and continually "tuning" the program to

building and racing exotic cars.  "There aren't many practical

uses for dragsters or Formula 1 race cars.  But some things

engineers do to make those cars perform better eventually find

their way into cars you and I drive," said Slowinski.



Slowinski noted that with the discovery of the new prime

number, a new "perfect" number can also be generated.  A

perfect number is equal to the sum of its factors.  For

example, 6 is perfect because its factors -- 1, 2 and 3 -- when

added together, equal 6.  Mathematicians don't know how many

perfect numbers exist.  They do know, however, that all

perfect numbers have a direct relationship to Mersenne primes. 

The new perfect number generated with the new Mersenne

prime is the 33rd known perfect number and has 517,430

digits.  The 32nd perfect number had 455,663 digits.



Cray Research creates the most powerful, highest quality

computational tools for solving the world's most challenging

scientific and industrial problems.



###