A Mersenne Prime is a special type of prime number that can be expressed in the form 2^p - 1, where p is also a prime number. For example, if p = 3, then 2^3 - 1 = 7, which is a prime number. Mersenne primes are named after the French monk Marin Mersenne, who studied these numbers in the early 17th century. Mersenne primes are significant in number theory and have applications in computer science, particularly in cryptography and random number generation. The search for new Mersenne primes is often conducted using distributed computing projects like the Great Internet Mersenne Prime Search (GIMPS), which has discovered many of the largest known prime numbers.