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Prime wonder: 9.1 million digits

Ian Sample

The largest prime number

London: If it takes 700 computers nine years to find the answer, it must be one beast of a question. But for researchers in Missouri, on a quest to find the world's largest prime number, it was all worth the while. In mid-December, a reassuring beep signalled the end of the long search, and one of the computers came up with a prime number with the mysterious name of M30402457. Made up of 9.1 million digits, it trounces all the others discovered so far.

Prime numbers are positive numbers divisible only by themselves and the number one, such as 1, 2, 3, 5 and 7. The number discovered in Missouri falls into a special category called mersenne prime numbers. These are expressed as the number 2 raised to the power of `p' minus one, where `p' is also a prime number.

Moment to remember

For Steven Boone and Curtis Cooper at the Central Missouri State University, it was a moment to remember. "It's a huge achievement, we're really excited," said Dr. Boone. "People ask why we do this. It's like going on a quest. We're looking for something incredibly rare," he said. "It's the icing on the cake." And then there is the financial incentive. The person who finds the first mersenne prime number more than 10 million digits long stands to win $100,000 (about Rs. 45 lakhs), the prize in the Great Internet Mersenne Prime Search competition.

Series of computers

The researchers began by commandeering a few hundred of the university's computers to crunch away at the problem. In the nine years since, the number of computers joining the hunt grew to 700. The algorithms used in the search were sent out to computers around the college campus and run quietly in the background without the user noticing. The programs work through increasingly higher numbers and test each one to see if it is a mersenne prime.

"At first, it would take one computer three months to check one number. Now, we've more powerful computers, so it's taking around 25 days for each number, but the higher we go, the more calculations we need to do," said Dr. Boone. To confirm their number was prime took 30 million separate calculations.

The latest number beats the figure discovered by Martin Nowak, a German eye specialist with a passion for mathematics, by more than a million digits. His number, revealed in March last year, was a mere 7.8 million digits long. —

© Guardian Newspapers Limited 2004

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