We just found a new one, and it has seven million digits. Here is the bottom line:
Mersenne primes are an especially rare type that take the form 2^p-1, where p is also a prime number. They are named after a 17th Century French monk who first came up with an important conjecture about which values of p would yield a prime. The new number can be represented as 2^(24,036,583)-1. It is the 41st Mersenne prime to have been found.
Here is the full story.
Note also that the number was found by a consortium of private computers, designed to exchange spare computing power:
GIMPS volunteers download a piece of software that runs in the background on their computer. A central server distributes different prime number candidates to each machine, which use spare processing power to test whether it is a genuine prime or not.