A particular class of prime numbers is known as Mersenne
Chapter 2, Problem 47(choose chapter or problem)
A particular class of prime numbers is known as Mersenne primes, named for a French monk and mathematician of the seventeenth century who studied them. Mersenne primes are numbers of the form \(2^p − 1\) where p is a prime, but not all numbers of this form are primes. For example, \(2^{11} − 1 = 23 \cdot 89\) is not prime. The largest known prime number as of June 2013 is \(2^{57,885,161} − 1\), a Mersenne prime. There happens to be a particularly efficient algorithm for testing numbers of the form \(2^p − 1\) for primality, which is why almost all of the largest known primes are Mersenne primes. In recent years, most of these Marsenne primes have been discovered (and verified) by the GIMPS (Great Internet Mersenne Prime Search) distributed computing project, a worldwide group of volunteers who collaborate over the Internet to test for
Mersenne primes.
Find the first 4—the 4 smallest—Mersenne primes.
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