Curtis Cooper from the University of Central Missouri has discovered the largest known prime number as part of the Great Internet Mersenne Prime Search (GIMPS). An integer greater than one is called a prime number if its only divisors are one and itself. For, example the first prime numbers are 2,3,5,7 and 11. The record prime number, 257,885,161-1, has 17,425,170 digits.
According to a news release from the project, GIMPS is the longest continuously-running global “grassroots supercomputing” project in Internet history.
“It’s analogous to climbing Mount Everest,” George Woltman, the man who founded GIMPS, told LiveScience. “People enjoy it for the challenge of the discovery of finding something that’s never been known before.”
This is the third record prime for Professor Cooper and the University of Central Missouri. Their first record prime was found in 2005 and bested by their second record prime in 2006. With this discovery, the University of Central Missouri reclaims the record from mathematicians at UCLA who grabbed the record with a 12,978,189 digit prime number in 2008. Professor Cooper’s finding is reportedly eligible for a $3,000 GIMPS research discovery award.
“It’s sort of like finding a diamond,” Chris Caldwell at the University of Tennessee, Martin, told the New Scientist. “For some reason people decide they like diamonds and so they have a value. People like these large primes and so they also have a value.”
According to the news release, the new prime number is a member of a special class of extremely rare prime numbers known as Mersenne primes. The 17-million-digit prime number is only the 48th known Mersenne prime ever found. This class of rare prime numbers was named for the French monk Marin Mersenne, who examined these numbers more than 350 years ago.
There is an interesting history to the arithmetic algorithms underlying the GIMPS project. The software that helped discover the largest Mersenne prime is based on a special algorithm. In the early 1990’s, Richard Crandall came up with ways to double the speed of what are called convolutions, which are essentially big multiplication operations. Woltman implemented Crandall’s algorithm in assembly language, creating a prime-search program of exceptional efficiency.
GIMPS, founded in 1996, has discovered all 14 of the largest known Mersenne primes. Volunteers can download a free program to look for these primes with a cash award given to anyone who can compute a new prime.
To make sure there were no errors in the prime discovery process, the new prime number was independently verified using different programs running on different hardware.
The GIMPS software was created by Woltman. Scott Kurowski wrote and maintains the PrimeNet system that coordinates all the GIMPS clients.
Volunteers can earn research discovery awards of $3,000 or $50,000 if their computer finds a new Mersenne prime. The organization hopes to someday win the $150,000 award handed out by the Electronic Frontier Foundation for locating a 100-million-digit prime number.
GIMPS notes that there may be smaller, as yet undiscovered Mersenne primes, and there definitely are larger Mersenne primes waiting to be discovered by anyone with a reasonably powerful PC. All the necessary software can be downloaded for free here.