Record size 17.4 million-digit prime found

Wednesday, February 6, 2013

Curtis Cooper, a mathematician and computer science professor at the University of Central Missouri, has discovered the largest known prime number to date on January 25. Several people verified the discovery using different hardware and software by the beginning of February and it was announced on Tuesday. Cooper found the prime as a participant in the distributed computing project known as the Great Internet Mersenne Prime Search, or GIMPS. Cooper runs the GIMPS client, called Prime95, on an estimated 1,000 computers at the university.

The number was first reported to the GIMPS server on January 25 from a university computer which had been running 39 days non-stop. However as for any Mersenne prime candidates, the discovery was announced after several people have verified the number using different hardware and software. The three independent verifications took from three to seven days of computation on powerful hardware.

A prime number is a positive integer greater than 1 that can only be evenly divided by 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17 and 19. 77 (for example) is not prime because it is a product of 7 and 11. The newly discovered prime is expressed as 2^57,885,161 − 1 and has 17,425,170 digits. It is a specific type of prime number called a Mersenne prime, which are of the form 2^p − 1. The exponent p must be prime for the number to be prime. As of February 2013, there are only 48 known Mersenne primes.

George Woltman developed and founded GIMPS, the longest known continuously running computer project, in 1996. Cooper as a participant had previously discovered two other Mersenne primes, 2^30,402,457 − 1 in December 2005 and 2^32,582,657 − 1 in September 2006, with fellow professor Steven Boone. This latest discovery ends an intermission of almost four years; the previous Mersenne prime was found in April 2009.

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Sources

George Woltman. "GIMPS press release" — Great Internet Mersenne Prime Search, February 5, 2013
Jacob Aron. "New 17-million-digit monster is largest known prime" — New Scientist, February 5, 2013

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