Only 51 Have Been Found: Here’s Mersenne Primes
And, so what’s the next number in the sequence 3, 7, 31, and 127? Well, it’s 8,191, and I will explain why in a little minute.
If you need to test with prime numbers — such as with public key encryption — how do you remember some large ones that you can test with? Well, one of the easiest ways is to remember the Mersenne prime numbers.
Mersenne prime numbers were first defined by Marin Mersenne and who was a 17th Century French Minim friar. His main contribution included his investigations of prime numbers, along with being seen as the father of acoustics. A Mersenne prime is defined as a prime number that is one less than a power of two. The general form is M_n=2^n−1 where n is an integer. The discovery of 2¹¹²¹³-1 was even given its own postmark:
The largest found is 2⁸²⁵⁸⁹⁹³³-1, and is the 51st Mersenne prime to be ever found). Since 1997, the Great Internet Mersenne Prime Search (GIMPS) distributed system has been used to find new Mersenne primes.
From Wikipedia, here are the first 20:
The Mersenne sequence becomes:
2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521…
