The Largest Known Prime

References:

• Largest Know Prime at WikiPedia

• The Largest Know Primes - a Summary

• Mersenne prime

This is the largest known Mersenne Prime:

2^57,885,161 -1

As of October 2014, 48 Mersenne primes are known.

Given that p is prime it is possible that

Mp=2^p -1

is prime. But you have to test it, prove it so. For example

M11=2^11 -1 = 2047 = 23 * 89

is a Mersenne number that is not prime.