A mathematical treasure hunt Numbers: The search for world-record prime numbers has captured the imagination of everyone from grade-schoolers to computer experts.

Sun Journal

November 08, 1998|By Michael Stroh | Michael Stroh,SUN STAFF

It just didn't add up.

Technicians at U.S. West, the Denver-based telephone company, couldn't understand last May why directory-assistance computers were grinding away for minutes to find phone numbers when they normally needed seconds. At one point, the slowdown even threatened to shutter the company's Phoenix service center. What was going on?

Alarmed that hackers were afoot, U.S. West scrambled its Intrusion Response Team. The squad of computer experts combed through the company's labyrinthine computer network and found a mysterious software program running on more than 2,500 machines. The scope of the intrusion was worrisome. Even more startling was this: The unauthorized software wasn't stealing sensitive account numbers or shredding computer files.

It was hunting for prime numbers.

Someone, it seemed, was tapping into U.S. West's powerful computer network to create not mayhem but mathematics.

The company eventually traced the software to 28-year-old Aaron Blosser, a U.S. West computer consultant and self-described "math geek." Blosser admitted installing the software but insisted that it posed no threat.

"I've worked on this problem for a long time," he told the Denver Post soon after FBI agents raided his house and seized thousands of dollars worth of computer equipment. "When I started working at U.S. West, all that computational power was just too tempting for me."

The strange case of Aaron Blosser, who has yet to be charged with a crime but remains under FBI investigation, has brought to light an unusual and little-known mathematical treasure hunt taking place around the globe. It's called the Great Internet Mersenne Prime Search -- GIMPS for short -- and it has captured the imagination of everyone from grade-schoolers to Ph.D.s. Their goal: to hunt down world-record prime numbers.

"Sure, we seek records that are harder for folks to understand than 70 home runs," says Chris Caldwell, a mathematician at the University of Tennessee who also hunts for primes in his spare time. "But competition seems to run in human nature. We each seek our own spot in this strange world."

Prime numbers -- whole numbers evenly divisible only by 1 and themselves -- have beguiled mathematicians for centuries. Around 330 B.C. the Greek mathematician Euclid showed that )) an infinite number of primes exist but they occur in no logical pattern. The discovery touched off a race to find ever larger primes, a race that has lasted to this day.

Today most record-seekers focus their attention on Mersenne primes. These special prime numbers are the Hope diamonds of the mathematical world, as large as they are rare. Named after the 17th-century French mathematician Marin Mersenne, they are primes that fit the form 2 to the nth power minus 1, where n is also a prime. The first three Mersenne primes, for example, are 3 (2-1), 7 (2-1), and 31 (2-1).

Just 37 have been found in all of human history. The most recent-- 2-1 -- was unearthed in January by a 19-year-old California State University student using PCs in the campus computer lab. It measured a whopping 909,526 digits long, making it the largest Mersenne prime yet found. If written in newsprint, it would stretch more than two miles and require a week to recite aloud.

Until recently it took a supercomputer to flush out these elephantine numbers. But in 1996 a retired Orlando computer programmer and a California engineer devised a way to use home computers to find them. The idea was to link PCs together through the Internet, turning them into a single, massively parallel supercomputer. They wrote the software and the Great Internet Mersenne Prime Search was born.

Today more than 4,000 number lovers around the world are using the GIMPS software to hunt for Mersenne primes, each vying for 15 minutes of fame and a $1,100 cash prize. Collectively, the group churns through 280 billion calculations per second, a computing punch roughly equivalent to five of the world's most powerful supercomputers working full-steam.

The GIMPS software is designed to look for primes when its host PC isn't occupied with other tasks. It pulls an untested number off the GIMPS Web site (www.mersenne.org), and then grinds through a special mathematical formula to determine whether it is prime. The calculations can take days or weeks to complete. If the number turns out to be a dud, the process is repeated. But if it turns out to be prime, it could mean fame and fortune.

Just ask Landon Noll. In 1978 he was a high school senior when he and a classmate stumbled upon two Mersenne primes using a mainframe computer at a nearby community college. "It was a major life-changing experience for me," says Noll, now a 38-year-old number theorist at Silicon Graphics in Sunnyvale, Calif. "It sort of said, 'I've arrived.' "

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