TITLE: Do Mersenne numbers occur in fields of mathematics other than Number Theory?
QUESTION [6 upvotes]: Do Mersenne numbers turn out to be interesting in other fields of mathematics besides Number Theory? 

In other words, are the primes occuring in the sequence
$$M_n=2^n-1$$
or the recursive realtion
$$M(n+1)=2\times M(n)+1$$
useful in other fields of mathematics to solve problems or appear in the definition of other important functions?
I apologize in advance for any mistakes in my English, I hope that the translator did a good job :).

REPLY [3 votes]: Quoting from Wikipedia, "The Mersenne twister is a pseudo random number generator.... It provides for fast generation of very high-quality pseudorandom numbers, having been designed specifically to rectify many of the flaws found in older algorithms. Its name derives from the fact that period length is chosen to be a Mersenne prime."