September
13, 1997
by I. Peterson
As one of about 1,700 participants in the Great Internet Mersenne Prime Search (GIMPS), Gordon Spence had a choice of numbers to test. One of the numbers that he happened to pick turned out to be a record-breaking prime -- the largest number yet identified that is evenly divisible only by itself and 1.
An information technology manager at Thorn Microwave Devices in Hayes, England, Spence used software written by computer programmer George Woltman of Orlando, Fla., to determine that 2^2,976,221 - 1 is a prime number. If printed out, this 895,932-digit behemoth would fill 450 pages of a paperback book. It is more than twice as long as the previous record holder, found last November. Remarkably, Spence used a modest Pentium-based desktop computer to find the record prime. It took 15 days of calculation to obtain the result, which was later verified independently on a supercomputer. Woltman, who organized GIMPS more than a year ago, announced the discovery last week.
The new champion is also the 36th Mersenne prime to be found. Expressed in the form 2^p - 1, where the exponent p is itself a prime, Mersenne numbers have characteristics that make it relatively easy to determine whether a candidate is a prime. All the Mersenne numbers having exponents smaller than 2,976,221 have not been checked, so another Mersenne prime may yet lurk between the present record holder and the previous largest prime.
Aside from offering the thrill of holding a world record, however briefly, searches for huge primes have led to improved methods of multiplying large numbers, an operation crucial in many scientific and engineering applications. The Intel Corp. in Santa Clara, Calif., uses a modified version of Woltman's program to help detect manufacturing defects in its Pentium chips.
Because a program for testing primes constantly uses key parts of a microprocessor and stores and retrieves huge amounts of data, the chips can generate a greater than normal amount of heat, which sometimes causes failures. Roughly 2 to 4 percent of all machines used in the GIMPS project run into problems, Woltman says.
There are more Mersenne primes to be found, Woltman notes. Anyone with a reasonably powerful computer can join the hunt (http://www.mersenne.org/). "If we could use all the computing power that was wasted on screen savers, we could move a lot further forward," adds mathematician Chris K. Caldwell of the University of Tennessee at Martin.
References:
The official announcement of the discovery is available at http://www.mersenne.org/2976221.htm.
Further Readings:
Peterson, I. 1996. Another record prime. Science News Online (Dec. 14).
______. 1996. Mining prime terrain. Science News Online (Sept. 14).
Additional information about Mersenne primes can be found at http://www.utm.edu/research/primes/mersenne.shtml.
Information on joining the Great Internet Mersenne Prime Search is at http://www.mersenne.org/.
Sources:
Chris K. Caldwell
Mathematics and Computer Science
University of Tennessee at Martin
Martin, TN 38238
Website: http://www.utm.edu/~caldwell
Gordon Spence
Thorn Microwave Devices
Swallowfield Way
Hayes, Middlesex UB3 1DQ
United Kingdom
Website: http://www.rugeley.demon.co.uk/gimps/prime.htm
George Woltman
E-mail: woltman@magicnet.net
Website: http://www.mersenne.org/
Table of Contents -
September 13, 1997
