Prime time for supercomputers.

How do you put a new supercomputer through its paces to ensure that it's not making any mistakes? One way is to let it look for gigantic prime numbers. Such a test recently led to the largest prime yet discovered -- a 65,050-digit number that, when written out, would fill almost eight pages of this magazine.

The number is the 30th known example of a Mersenne prime, a number divisible only by 1 and itself and written in the form 2.sup.p--1, where the exponent p is also a prime number. For instance, 127 is a Mersenne number for which the exponent is 7. The record prime number's exponent is 216,091.

The accidental discovery occurred on a new, $10 million Cray X-MP supercomputer being tested at Chevron Geosciences Co. in Houston. Using a special computer program that checks for Mersenne primes while giving the computer a good workout, Chevron engineers happened to select a starting number that worked out. The supercomputer took about three hours to complete the 1.5 trillion calculations involved.

"It's really a hit-or-miss thing," says David Slowinski of Cray Research, Inc., in Minneapolis. Slowinski wrote the prime-finding program used at Chevron. "Everybody's surprised when you get one," he says. "There's always luck involved."

But the discovery had to be verified. That task fell to Stephen K. McGrogan of Elxsi in San Jose, Calif. Using one of his company's computers and his own program for checking for prime numbers, McGrogan took nine days of computer time to confirm the discovery.

What isn't clear is whether other Mersenne primes lurk in the gaps between those now known. The 29th Mersenne prime was also discovered by accident using a Cray supercomputer. "One of the things that I'm doing is a systematic search through lower number space to determine if any have fallen through the cracks," says McGrogan. Furthermore, he's developing an algorithm that may significantly speed up the process of testing for prime numbers.

Slowinski, in his spare time, is also tinkering with his prime-finding program. His fourth version of the program is now 30 times faster than the original. A version for the new Cray-2 supercomputer, a significantly faster machine than the Cray X-MP, is in the works.

For the 10 or 20 players who chase after Mersenne primes, the pursuit seems to be a kind of "insanity," says McGrogan. For the Chevron engineers, the prime-finding program is a good test before their new supercomputer takes on its real job of analyzing geological data collected during oil exploration.