About Mersenne Primes
Definition
A Mersenne prime is a prime number of the form 2p - 1, where p is also prime.
Examples: 3 = 2²-1, 7 = 2³-1, 31 = 2⁵-1
Current Status
As of 2024, 51 Mersenne primes are known. The largest is 282,589,933 - 1, with over 24 million digits!
The Challenge
Finding new Mersenne primes is computationally intensive. The Great Internet Mersenne Prime Search (GIMPS) coordinates distributed computing efforts.
Known Small Mersenne Primes
2²-1 = 3, 2³-1 = 7, 2⁵-1 = 31, 2⁷-1 = 127, 2¹³-1 = 8191, 2¹⁷-1 = 131071, 2¹⁹-1 = 524287