Mersenne Prime

A Mersenne prime is a Mersenne number that is a prime number. It is necessary for n to be prime for 2^n-1 to be prime, but the converse is not true.

For example, 31 = 2^5 − 1, and 5 is a prime number, so 31 is a Mersenne number; and 31 is also a Mersenne prime because it is a prime number. But the Mersenne number 2047 = 2^11 − 1 is not a prime because it is divisible by 89 and 23. And 2^4 -1 = 15 can be shown to be composite because 4 is not prime.

There are currently 44 Mersenne Primes.Some of the Mersenne primes are

3,7,31......................124575026…053967871(9,808,358 digits)

To know more about Mersenne Primes visit

http://www.mersenne.org/
http://mathworld.wolfram.com/MersenneNumber.html