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Old 2014-12-19, 14:11   #1
wildrabbitt
 
Jul 2014

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Default 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
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Old 2014-12-19, 16:26   #2
Mini-Geek
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"Tim Sorbera"
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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.
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Old 2014-12-19, 19:15   #3
wildrabbitt
 
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thanks
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Old 2014-12-19, 20:50   #4
Prime95
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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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