12,978,189-digit prime number discovered by UCLA researchers

Posted by Samantha Rose

Los Angeles (CA) - Mathematicians at UCLA discovered the 45th known Mersenne prime with almost 13 million digits. The discovery makes the group eligible for a $100,000 prize, which was promised for discovering the first prime with more than 10 million digits.
 
The UCLA researchers said that they found the 45th known Mersenne prime on a 75 computer network running Windows XP. The number was then verified on a different computer system that was running a completely different algorithm.

Thousands of people and groups all over the globe have been participating in the Great Internet Mersenne Prime Search, or GIMPS, a distributed computing network where underused computing power is harnessed to perform the calculations that are needed to find and verify that a number is in fact a Mersenne prime.
 
Edson Smith, the leader of the UCLA team said that his research group was delighted but already has begun “looking for the next one, despite the odds.” It was the eighth Mersenne prime discovered at UCLA.

Prime numbers are ones such as three, seven, and eleven that are only divisible by themselves and 1.

Mersenne primes are named after the 17th century French mathematician Marin Mersenne. These numbers are expressed as 2P-1 or two to the power of “P” minus one. P itself is in fact a prime number. For the newest prime number, P is 43,112,609 and the prime number is written as 243,112,609 − 1

The Electronic Frontier Foundation has offered the $100,000 prize for discovering the first Mersenne prime with more than 10 million digits. GIMPS, which will collect the prize money, said it will give $50,000 of the EFF award to the UCLA Mathematics Department for discovering the first 10 million digit prime. $25,000 will go to charity, and most of the remainder will go to discoverers of the previous six Mersenne primes.

UCLA said that the 12,978,189 digit number was found on August 23, 2008 as the 45thknown Mersenne prime. The research team narrowly beat Hans-Michael Elvenich, a 44 year old “prime number enthusiast” and an electrical engineer working for Lanxess, a chemical company in Germany, who discovered the 46th Mersenne prime with 11,185,272 digits (237,156,667-1) on September 6. GIMPS noted that this prime was the first Mersenne prime to be discovered out of order since Colquitt and Welsh discovered 2110,503-1 in 1988.

The first Mersenne prime number with 10 digits was discovered in 1772 by Leonhard Euler, the first with more than 100 digits (157) by Raphael M. Robinson in 1952, the first with more than 1000 digits (1281) by Alexander Hurwitz, the first with more than 10,000 digits (13,395) by Harry Nelson and David Slowinski in 1979, the first with more than 100,000 (227,832) by David Slowinski and Paul Gage in 1992 and the first with more than 1 million digits by Nayan Hajratwala as part of the GIMPS project in 1999.