UCLA mathematician Edson Smith and colleagues have found a really, really large prime number: it's 13 million digits long!
The group found the 46th known Mersenne prime last month on a network of 75 computers running Windows XP. The number was verified by a different computer system running a different algorithm. [...]
Mersenne primes — named for their discoverer, 17th-century French mathematician Marin Mersenne — are expressed as 2P-1, or two to the power of "P" minus one. P is itself a prime number. For the new prime, P is 43,112,609.
Thousands of people around the world have been participating in the Great Internet Mersenne Prime Search, or GIMPS, a cooperative system in which underused computing power is harnessed to perform the calculations needed to find and verify Mersenne primes.
Link - Thanks cjdavis!
To visualize how large the prime number 243,112,609 - 1 really is, if you print out the number at 75 digits per line and 50 lines per page, it would be almost 3,500 pages long!