Chris,
on your website http://www.utm.edu/research/primes/notes/faq/NextMersenne.html,
you say:
"This means that the geometric mean of two successive mersenne
exponents is 2 raised to 1/e^gamma or about 1.47576."

The definition of geometric mean of two numbers a and b is:
sqrt(a*b)
Therefore the geometric mean must be between a and b.  
I think that you mean that the geometric mean of two successive mersenne 
numbers is 2 raised to the (1/e^gamma) raised to the index of the mersenne 
numbers. 
-Lucas Wiman
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