Mersenne prime (or Marsenne prime)

A Mersenne (also spelled Marsenne) prime is a specific type of prime number. It must be reducible to the form 2 ⁿ - 1, where n is a prime number. The term comes from the surname of a French monk who first defined it. The first few known values of n that produce Mersenne primes are where n = 2, n = 3, n = 5, n = 7, n = 13, n = 17, n = 19, n = 31, n = 61, and n = 89.

With the advent of computers to perform number-crunching tasks formerly done by humans, ever-larger Mersenne primes (and primes in general) have been found. The quest to find prime numbers is akin to other numerical searches done by computers. Examples are the decimal expansions of irrational numbers such as pi (the circumference-to-diameter ratio of a circle) or e (the natural logarithm base). But the 'next' prime is more difficult to find than the 'next' digit in the expansion of an irrational number. 

It takes the most powerful computer a long time to check a large number to determine if it is prime, and an even longer time to determine if it is a Mersenne prime. For this reason, Mersenne primes are of particular interest to developers of strong encryption methods.

In August 2008, Edson Smith, a system administrator at UCLA, found the largest prime number known to that date. Smith had installed software for the Great Internet Mersenne Prime Search (Gimps), a volunteer-based distributed computing project.  The number (which is a Mersenne prime) is 12,978,189 digits long. It would take nearly two-and-a-half months to write out and, if printed, would stretch out for 30 miles.

Learn More About IT:
> Wikipedia has an entry about Mersenne primes.
> See Mersenne Primes: History, Theorems and Lists.
> The Guardian explains 'Why 2 to the power of 43112609 - 1 = $100000 for prime number hunters.'