Original URL: http://www.theregister.co.uk/2008/08/29/45th_mersenne_prime_discovered_maybe/

## 45th Mersenne prime discovered (possibly)

Move over 2^{32,582,657}-1. Your day has ended

Posted in Science, 29th August 2008 19:02 GMT

Distributed computing hasn't folded us a cure for cancer yet, but these projects in which PC users donate their spare processing power to solve scientific problems have unquestionably made major strides in uncovering ridiculously large prime numbers.

Fans of bountiful digits may soon be rocked by the potential discovery of the 45th known Mersenne prime. Details are still pretty scarce, but on August 23, the Great Internet Mersenne Prime Search (GIMPS) said a computer participating in the project has reported to have found the record-breaking number.

Marin Mersenne

Mersenne primes are named after the 17th century French ~~monk, scholar, scientist, mathematician~~ nerd Marin Mersenne. A Mersenne number is a number that is one less than a power of two, or M_{n} = 2^{n} – 1. So, the first few are 1, 3, 7, 15, 31, 63, and so on. Mersenne primes are Mersenne numbers that are also prime, meaning they are divisible only by 1 and itself.

You can see why finding these numbers have such a cult following.

Distributed computing has been a boon for Mersenne prime discovery, as the digits in the numbers quickly become extremely large and difficult to verify. GIMPS is presently responsible for 10 record breaking prime numbers, having found the 35th through 44th largest known.

As according to GIMPS protocol, the potential 45th Mersenne prime will not be officially disclosed until it has been verified as a prime. The leader of the project, George Woltman, unfortunately was on holiday when the number was reported, so the verification process didn't begin until the 26th. He estimates completion on September 12 and September 16.

To give an idea of the scale of these latest record-breaking numbers, the 44th Mersenne prime is 2^{32,582,657}-1, which works out to be 9,808,358 decimal digits long. That's 650,000 digits larger than the previous record and is presently the largest known prime number of any kind.

The 45th Mersenne prime may qualify for a $100,000 prize offered by the Electronic Frontier Foundation to anyone who discovers a prime number with at least 10 million digits. If GIMPS claims the reward, it plans to donate $25,000 to charity and give a large portion to the participant that discovered the prime number. ®