After I first learned about prime numbers as a kidlet, I became quite fond of them — a fondness that continues to this day, although I cannot explain why they are so appealing. But even amongst those special numbers that are prime, there is another, much smaller, group of numbers; the Mersenne prime numbers.
Named for Marin Mersenne, the French monk who began to study these numbers in the early 17th century, a Mersenne number (M) is defined as a positive prime integer (p) that is one less than a power of two:
for example;
M2 = 22 = 4 – 1 = 3
which is the smallest of the Mersenne primes. The next Mersenne prime is M3 = 7 and the third smallest Mersenne prime is M5 = 31.
Currently, only 47 Mersenne primes have been identified, and in fact, the largest known prime number, 2243,112,609 – 1, is a Mersenne prime. You’ll forgive me if I don’t write this number out for you, because this prime number is the first discovered to have more than 10 million base-10 digits.
Posted by Den 
