Mersenne Primes

Mersenne primes are a special type of prime number that can be written 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 prime, making it a Mersenne prime. These numbers are interesting because they are closely connected to perfect numbers and have unique mathematical properties. Many mathematicians search for the largest Mersenne primes, as they help verify number theory conjectures and improve on algorithms for testing primality.