The world's largest prime number just got much, much bigger. Say hello to 2^{57,885,161}-1, a prime number that is over 17 million characters long when written out in full—enough to fill 13,000 pages of A4 paper.

According to New Scientist, it breaks a four-year dry spell which saw no new prime numbers being found. It was discovered by Curtis Cooper at the University of Central Missouri in Warrensburg, who is part of the Great Internet Mersenne Prime Search. Yes, that is GIMPS for short. Stop sniggering.

Anyway, the new prime is itself one of the mystical Mersenne primes: prime numbers which have the form 2^{p} - 1, where p is itself a prime number. New Scientist explalins:

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

^{43,112,609}- 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.

The new number, in all its 17 million digit glory, is almost impossible to picture. If you're after some way to visualize it, it would take up a staggering 13,000 pages of A4 paper. That's some bedtime reading.

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While there are theoretically an infinite number of primes, finding them is a laborious business. GIMPS uses distributed computing to hunt them out, but with each new find the search for the next becomes harder—so expect a wait before the next one appears. [New Scientist]

*Image by re-birf under Creative Commons license*