A Mersenne number is a special type of number that is expressed in the form M_n = 2^n - 1 , where n is a positive integer. These numbers are named after the French monk Marin Mersenne, who studied their properties in the early 17th century. Mersenne numbers are significant in number theory and are often used in the search for prime numbers. Some Mersenne numbers are prime, meaning they have no divisors other than 1 and themselves. For example, when n = 3 , the Mersenne number M_3 = 2^3 - 1 = 7 , which is prime. The search for larger Mersenne primes continues today, often using advanced computing techniques and projects like the Great Internet Mersenne Prime Search (GIMPS).