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Old 2007-09-04, 14:04   #1
jasong
 
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"Jason Goatcher"
Mar 2005

66638 Posts
Default 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^n-1)

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 2007-09-04 at 14:15 Reason: Added second question
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