20070904, 14:04  #1 
"Jason Goatcher"
Mar 2005
3×7×167 Posts 
odds of a Mers. prime being found in a range of n.
Is the following true? Or, at least, assumed to be true?
odds of a random n yielding a Mersenne prime: ln(n)*ln(2^n1) I had a hell of a time coming up with the qualifier(the second line). Corrections are appreciated and encouraged. Btw, I put this in Information and Answers because it's fairly simple math, and I feel that a lot of people that might not normally visit the Math forum might be interested in this, since it has to do with Mersenne numbers. Edit: Another question: Assuming GIMPS throughput increases at a sustained rate, basically a parabolical curve, will our speed at finding primes be likely to increase, decrease, or stay exactly the same? (Maybe this one should go in Math, and the answer should come back here when it's decided upon) Last fiddled with by jasong on 20070904 at 14:15 Reason: Added second question 
20070904, 15:15  #2  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
10266_{8} Posts 
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20070904, 16:42  #3 
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×3×7×89 Posts 
This question is anything BUT simple math. The question involves
VERY deep questions in analytic number theory and the true answer isn't even known, let alone proven. It is *conjectured* on the basis of some heuristics that Mersenne primes are Poisson distributed and that the expected number of Mersenne primes between 2^n and 2^(n+1) is exp(gamma) as n > oo. However this conjecture is not very "firm". It is more of an open question than a true conjecture (like (say) the twin prime conjecture). 
20070905, 23:35  #4  
"Jason Goatcher"
Mar 2005
3×7×167 Posts 
I apologize,
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