Which is the largest prime number?

If you are referring to the largest "known" prime number,
presently it is 2^ 37,156,667-1, an 11,185,272 digit number which was found in Sep 2008
by Hans-Michael Elvenich in Langenfeld near Cologne,
Germany.

Any prime number can be expressed in the form 2^p
- 1, where p is also a prime, though it is not necessary that every number of the form
2^p - 1, where p is a prime is a prime number.

The numbers
of the form 2^p -1 are known as Mersenne prime numbers. With an increasing ability to
harness large amounts of computing power it is now possible to calculate larger prime
numbers which are Mersenne prime numbers.