Do Mersenne numbers occur in fields of mathematics other than Number Theory?

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 :).

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They're great for making really bad RSA keys. –  Alexander Gruber Mar 22 '13 at 21:09
see this Wikipedia page... –  Coffee_Table Mar 22 '13 at 21:28
What do you mean? Using two mersenne numbers in the RSA algorithm generates weak keys? –  MphLee Mar 22 '13 at 21:35
@Coffee_Table :thanks but the section "Mersenne numbers in nature and elsewhere" is not very rich, for that I asked here. –  MphLee Mar 22 '13 at 21:54
A generalization is the "repunits": Mersenne numbers are numbers of the form "111...1" in base 2; the analoguous exists for other bases. Let b be another base then ${ b^n - 1 \over b - 1}$ gives numbers, which are repunits in the digitrepresentation of that number system. So search for keywords "repunits" and also "cyclotomic polynomials" to find possibly more interesting stuff ... –  Gottfried Helms Mar 23 '13 at 9:07