Mathematical frontiersUCLA group discovers largest Mersenne prime yet

You may recall from Math 101 in college that a Mersenne number is a positive integer that is one less than a power of two (in other words, numbers such as 3, 7, and 11 which are divisible by only two whole positive numbers: themselves and one):

M_n = 2ⁿ - 1

Note that some definitions of Mersenne numbers require that the exponent n be prime. A Mersenne prime is a Mersenne number which is prime. As of 6 September 2008, only 46 Mersenne primes are known, and the largest known prime number — 2^43,112,609 - 1 — is a Mersenne prime. In modern times, the largest known prime has almost always been a Mersenne prime.

This brings us back to 6 September and the 46th Mersenne prime. Mathematicians at UCLA have discovered a 13 million-digit prime number, a long-sought milestone which makes them eligible for a $100,000 prize. The group found the 46th known Mersenne prime last month on a network of 75 computers running Windows XP. The number was verified by a different computer system running a different algorithm. “We’re delighted,” said UCLA’s Edson Smith, the leader of the effort. “Now we’re looking for the next one, despite the odds.”

There must be something in the water at UCLA, because this is the eighth Mersenne prime discovered at the school by Bruins researchers. Thousands of people around the world have been participating in the Great Internet Mersenne Prime Search, or GIMPS, a cooperative system in which underused computing power is harnessed to perform the calculations needed to find and verify Mersenne primes.

The $100,000 prize is being offered by the Electronic Frontier Foundation (EFF) for finding the first Mersenne prime with more than 10 million digits. The foundation supports individual rights on the Internet and set up the prime number prize to promote cooperative computing using the Web. The prize could be awarded when the new prime is published, probably next year.