mersenneforum.org probabilty of finding a mersenne prime
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 2014-12-19, 14:11 #1 wildrabbitt   Jul 2014 3×149 Posts probabilty of finding a mersenne prime Hi, when I get some assignments from the GIMPS server I get an approximate probabilty of finding a MP. Does anyone know how the odds are worked out. My guess is that it uses the PNT. William
2014-12-19, 16:26   #2
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"Tim Sorbera"
Aug 2006
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4,271 Posts

http://www.mersenne.org/various/math.php mentions this at the end of the LL section.
Quote:
 This simplifies to 64 / 5000070 or 1 in 78126. This simple approach isn't quite right. It would give a formula of how_far_factored divided by (exponent divided by 2). However, more rigorous work has shown the formula to be (how_far_factored-1) / (exponent times Euler's constant (0.577...)). In this case, 1 in 91623. Even these more rigourous formulas are unproven.

 2014-12-19, 19:15 #3 wildrabbitt   Jul 2014 3·149 Posts thanks
 2014-12-19, 20:50 #4 Prime95 P90 years forever!     Aug 2002 Yeehaw, FL 25×35 Posts Prime95 also assumes if P-1 has been run it had a 3 or 4% chance of finding a factor (I'd have to look at the code). This improves your chances that the LL test will show the Mersenne number to be prime.

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