The new largest prime number has been discovered! Why is this awesome? Because it is more than 17 million digits long. Also, the article contains quotes from mefi's own escabeche.
In September 2006 the largest known prime number, a 9.8 million digit number, was discovered. If you find one over ten million digits you can win US$100,000 (of which you get to keep $50,000). No maths is required - just download the software and you're away. Warning: it takes about a month to run one primality check so some patience is required. Look out though Cooper and Boone look like they might beat you to it.
Find a 10 million digit prime number, get $100,000! "Now the bad news. Testing a single 10,000,000 digit number takes a full year on a 500 MHz Pentium III computer." This GIMPS organization merely provides software to do the searching process (not to mention they take most of the profits if you DO find a new prime).