Because 243,112,609-1 has the form 2n-1, it’s called a “Mersenne prime,” after a French monk born in the 16thcentury who made an (incorrect) conjecture about them. Mersenne primes are of particular interest partly because they can be expressed in such a compact form. (It sure is easier to write 243,112,609-1 than to type out all 13 million digits!) More significantly, though, some clever methods have been developed to identify them.
Like SETI@Home, GIMPS hooks together millions of PCs that donate their unused cycles to crunching the numbers for a very large computing project, in this case, finding these insanely huge prime numbers.
EFF is offering a $150,000 award for a prime with 100 million digits and $250,000 for 1 billion digits. But to get to these huge numbers, GIMPS will have to retool its distributed approach, says Landon Noll, a judge for the contest and a discoverer of the former biggest known prime. What's needed is an algorithm to let multiple computers work together to test a single prime, since testing a billion-digit number would take a single PC more than 500 years.