Student Finds Largest Known Prime Number

Thu Dec 11, 6:12 AM ET

By JIM IRWIN, Associated Press Writer

DETROIT - 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.

The number is 6,320,430 digits long and would need 1,400 to 1,500 pages to write out. It is more than 2 million digits larger than the previous largest known prime number.

Shafer, 26, helped find the number as a volunteer on an eight-year-old project called the Great Internet Mersenne Prime Search.

Tens of thousands of people volunteered the use of their PCs in a worldwide project that harnessed the power of 211,000 computers, in effect creating a supercomputer capable of performing 9 trillion calculations per second. Participants could run the mathematical analysis program on their computers in the background, as they worked on other tasks.

Shafer ran an ordinary Dell computer in his office for 19 days until Nov. 17, when he glanced at the screen and saw "New Mersenne prime found."

A prime number is a positive number divisible only by itself and one: 2, 3, 5, 7 and so on. Mersenne primes are a special category, expressed as 2 to the "p" power minus 1, where "p" also is a prime number.

In the case of Shafer's discovery, it was 2 to the 20,996,011th power minus 1. The find was independently verified by other participants in the project.

Mersenne primes are rare but are critical to the branch of mathematics called number theory. That said, what is the practical significance of Shafer's number?

"People are going to make posters of it to hang up on the wall," said Shafer, who is pursuing a doctorate in chemical engineering. "It's a neat accomplishment, but it really doesn't have any applicability."

As for his own standing in the world of mathematics, "I don't think I'm going to be recognized as I go down the street or anything like that."

He said the method by which the number was found — harnessing many computers together — is more important than the number itself.

"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."