DETROIT (AP) - More than 200,000 computers spent years looking
for the largest known prime number. It turned up on Michigan State
University graduate student Michael Shafer's off-the-shelf PC.

"It was just a matter of time," Shafer said yesterday. "You know
that it will pop up at some point."

That point, according to coordinators of the worldwide search
for the largest prime number, came after eight years and a combined
25,000 years of computer time. Shafer, 26, of DeWitt, joined the
research project called the Great Internet Mersenne Prime Search
(GIMPS) three years ago.

Shafer ran a Dell Dimension PC with 2 gigahertz of memory and an
Intel Pentium 4 microprocessor - "like you'd get at Circuit City" -
in his office for 19 days until Nov. 17, when he glanced at the
screen at 2:30 p.m. and saw "New Mersenne prime found."

A prime number is a positive number divisible only by itself and
one; the list begins with 1, 2, 3, 5, 7 and so on. In the case of
Shafer's discovery, the list went on and on and on, to 2 to the
20,996,011th power minus 1. The number is 6,320,430 digits long and
would need 1,400 to 1,500 pages to write out, he said.

Mersenne primes are expressed as 2 to the "p" power minus 1,
where "p" also is a prime number. They are rare but are critical to
the branch of mathematics called number theory, according to New
Scientist magazine.

That all said, what's the significance of Shafer's number?

"People are going to make posters of it to hang up on the wall,"
he said. "It's a neat accomplishment but it really doesn't have any
applicability."

Shafer, who earned his undergraduate degree at Michigan
Technological University and is pursuing a doctorate in chemical
engineering, said his discovery's true value is its contribution to
GIMPS.

The project linked 60,000 volunteers operating 211,000 computers
of all types and capacities, Shafer said.

"Somebody else could have found the number," he said. "You
install the program on the computer and it takes care of itself.
(But) I get the credit, along with the people that developed the
software."

By running free software developed by GIMPS founder George
Woltman of Orlando, Fla., and connecting to a server developed by
Scott Kurowski of San Diego, participants in effect created a
supercomputer able to perform 9 trillion calculations per second,
according to the GIMPS Web site.

"The prime number itself isn't all that important," Shafer said.
"What's more important is the method that goes into the process of
discovery ... how much can we accomplish having all these computers
working together?"

The Search for Extraterrestrial Intelligence is another example
of so-called folding, in which thousands of computers work in
tandem. GIMPS, Shafer said, "is probably the most successful
because it's had so many results."

Indeed, although Shafer's is only the 40th Mersenne prime ever
found, a larger one could be found "tomorrow (or) it might not be
for another five years," he said.

Because of that, Shafer said that his celebrity in computing
circles could be short-lived.

"I don't think I'm going to be recognized as I go down the
street or anything like that," said Shafer, who is interested in
studying renewable resources. "I'll still be involved in the
project but the nice thing is, it's automated so I don't have to
shift my focus or anything like that."