Mersenne Numbers

   I got recently introduced to the books of Keith Devlin. Keith stands almost in the category of Stewart and Courant. Most of his books do talk about Mersenne Numbers. So what are these Mersenne Numbers ? These are actually Prime Numbers of the form 2^N-1.  Mersenne was a monk and he made some starting revelations like for N equal to 2,3,5,7,13,19,31,67,127, 257 are prime along with a bold claim that there are no other numbers less than 257 which are prime. However he was not all correct. It was found out that 67 and 257 do not give prime and there are prime numbers at N equal to 61,89 and 107. But isn't it still surprising that Mersenne who was born in 17 Century could predict about such big numbers (recall tower of hanoi problem that how big 2^64 is !!)when computers were not there. So does he had some algorithm. Prime number prediction is attracting a lot of people because of its usefullness in Cryptography. Here is the home page http://www.mersenne.org/prime.htm of Mersenne prime number website. And as of today 41st number has been found and it shouldn't be far when someone finds the 42nd.  One thing about Prime numbers is that they are not distributed in a pattern (as of now, otherwise their prediction will be a lot more easy).