SHARCNet verifies largest-ever prime number

A volunteer with the Great Internet Mersenne Prime Search has a new notch on his résumé —— the discovery of the world’s largest prime number.

Josh Findley, an independent data architecture consultant

in Seattle, found the new number, expressed as 2 to the 24,036,583th power minus 1.

It belongs to a group of special numbers called Mersenne primes, named after Marin Mersenne, a 17th century French monk who first studied the rare numbers 300 years ago. A prime number can only be divided by one and itself, for example, the number three.

Finding the 41st known Mersenne prime was “”pretty easy, actually,”” according to Findley. “”I installed the software (downloaded from on my three machines . . . and as soon as they’re done testing one (number), they just grab another one from the server. So it’s just a program that I’ve been running for about five years.

“”The thing that’s kind of exciting is how quickly we found the next prime number. It was only six months ago, I think, when they found the last one.””

Findley, who explained Mersenne primes are the easiest large prime numbers to test for efficiently, became involved with GIMPS, the Great Internet Mersenne Prime Search, while researching prime numbers and distributed computing projects on the Web.

Large prime numbers, which can be used as applications in fields like data security, are expected to contribute to advances in cryptography and encryption algorithms. But for Findley, eager to search for new primes, finding the latest prime was simply a “”fun project that people interested in math or distributed computing projects can enjoy.””

Jeff Gilchrist, an IT security specialist at Elytra Enterprises Inc. in Ottawa, was one of the people who verified Findley’s discovery using systems at SHARCNet, a high-performance computing network connecting 11 academic institutions in south-central Ontario. (All prime numbers need to be verified to become official.)

“”Since the number is so large, over seven million digits, you have to use special software to do the actual verification,”” Gilchrist said, adding he used an open-source program. He explained there was a chance Findley’s computer had an error while it was running, giving him a false positive.

Although it took Findley two weeks to receive a positive result while testing 2 to the 24,036,583th power minus 1, Gilchrist explained he needed 10 or 11 days to test his number using four processors at SHARCNet.

George Woltman, founder of GIMPS and a retired computer programmer in Orlando, Fla., created the program needed for math enthusiasts to find huge prime numbers. He said GIMPS has already come across seven, but admitted the latest addition has no practical use now because numbers so large aren’t needed for cryptography.

“”There’s an infinite number of (prime numbers),”” Woltman said. “”The larger they are, the harder they are to find. It’s kind of luck of the draw as to who gets the number to test that actually turns out to be prime.””

GIMPS is searching for the first 10-million-digit prime (Findley’s finding was short by about three million digits) to claim a US$100,000 offered by the Electronic Frontier Foundation, an organization that defends digital rights.


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