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World's largest prime number has 17 million digits

February 07, 2013 14:37 IST

Researchers have identified the world's largest prime number yet, beating the previous record by over four million digits.

The number has now shot up to 2 multiplied by itself 57,885,161 times minus 1, breaking a four-year dry spell in the search for new, ever-larger primes.

Curtis Cooper from the University of Central Missouri in Warrensburg made the finding 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, the New Scientist reported.

"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," said Caldwell.

All prime numbers can only be divided by themselves and 1. The rare Mersenne primes all have the form 2 multiplied by itself p times minus 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, 2 multiplied by itself 43,112,609 times minus 1, which was also found by GIMPS in 2008, has just under 13 million digits.

All 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.

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 shift through each prime-number candidate in turn, until eventually one lucky user discovers a new prime.

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

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