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# Student discovers largest prime number

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.
/ Source: The Associated Press

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 Wednesday. "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 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 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."