Original URL: http://www.theregister.co.uk/2013/02/06/biggest_prime_number_ever_found/

## Boffins find 17,425,170-digit prime number

2^{57885161}-1 takes crown as biggest prime ever found

Posted in Science, 6th February 2013 03:04 GMT

The Great Internet Mersenne Prime Search (GIMPS) has struck again, finding the largest-ever Mersenne prime number.

The number, the 48th Mersenne prime found, is 17,425,170 digits long and therefore most comfortably represented as 2^{57885161}-1 . The previous record-holder was a mere 12,978,189 digits. If you want to read the whole thing, you can do so here, but be warned: a 22.45 megabyte download awaits.

Mersenne primes, as we've reported before are numbers of the form M_{n} = 2^{n} − 1, where n is an integer. 17th century French monk Marin Mersenne was rather fond of them.

So is Curtis Cooper, a professor at the University of Central Missouri who participates in GIMPS, a distributed prime number hunter that works in the mode made famous by alien-spotting app SETI@Home.

Both use individual PCs to work on small portions of larger tasks and collate results centrally.

Marin Mersenne

The GIMPS project says “primality proof took 39 days of non-stop computing on one of the University of Central Missouri's PCs” before tests using the same app, but on other hardware proved the result. An NVidia GPU took 3.6 days to do so, an Intel i7 CPU needed 4.5 days and a 32-core server chewed up another six days on the problem.

The existence of the colossal prime number is largely a curiosity, as while large primes are used for applications such as cryptography it's hard to imagine a 22 megabyte number being pressed into service.

A more likely reason for the ongoing pursuit of primes is the $US50,000 prize on offer to the finder of the first 100-million-digit prime number. ®