The largest known prime number has just shot up to 257,885,161 – 1, breaking a four-year dry spell in the search for new, ever-larger primes.

Curtis Cooper at the University of Central Missouri in Warrensburg made the find as part of the Great Internet Mersenne Prime Search (GIMPS), a distributed computing project designed to hunt for a particular kind of prime number first identified in the 17th century.

All prime numbers can only be divided by themselves and 1. The rare Mersenne primes all have the form 2p – 1, where p is itself a prime number.

The new prime, which has over 17 million digits, is only the 48th Mersenne prime ever found and the 14th discovered by GIMPS. The previous record holder, 243,112,609 – 1, which was also found by GIMPS in 2008, has just under 13 million digits. All of the top 10 largest known primes are Mersenne primes discovered by GIMPS. Until today, the most recent addition to the list was found in 2009, but it was smaller than the 2008 discovery.


Volunteer sifters

Though there are an infinite number of primes, there is no formula for generating these numbers, so discovering them requires intensive computation. GIMPS uses volunteers’ computers to sift through each prime-number candidate in turn, until eventually one lucky user discovers a new prime.

Cooper runs GIMPS software on around a thousand university computers, one of which spent 39 days straight proving that the number was prime. This was then independently verified by other researchers.

Though there is little mathematical value to finding a single new prime, these rare numbers are prized in their own right by some. “It’s sort of like finding a diamond,” says Chris Caldwell at the University of Tennessee, Martin, who keeps a record of the largest known primes. “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.”

Prime-hunting isn’t a completely esoteric pastime though, as these numbers underpin the cryptographic techniques used to make online transactions secure.

Prizes for primes

The Electronic Frontier Foundation, an internet civil liberties group, is offering prizes of $150,000 and $250,000 to the discovery of the first prime with at least 100 million and a billion digits, respectively. Previous prizes for primes 1 million and 10 million digits long have already been awarded.

Cooper will receive a $3000 prize from GIMPS for making the discovery.

Don’t expect to see the next largest prime any time soon though. The problem becomes harder over time, as larger primes are both more rare and harder to check. “Those two things work together to spread them out as time goes on,” says Caldwell.