probabilty of finding a mersenne prime

wildrabbitt · 2014-12-19, 14:11

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

Mini-Geek · 2014-12-19, 16:26

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.

wildrabbitt · 2014-12-19, 19:15

thanks

Prime95 · 2014-12-19, 20:50

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.

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

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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 2×53×71 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.