mersenneforum.org > Math I get 13% less primes than I expected:-(
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 2010-10-29, 16:47 #1 mart_r     Dec 2008 you know...around... 22·5·31 Posts I get 13% less primes than I expected:-( Suppose I have an integer of magnitude of about 1028. If this number has no factors less than 104, am I right in assuming that this leaves a chance of about log(1028)/(2*log(104)) = 1:3.5, i.e. 28.57%, that this number will be prime?
2010-10-29, 17:17   #2
axn

Jun 2003

2×32×269 Posts

Quote:
 Originally Posted by mart_r Suppose I have an integer of magnitude of about 1028. If this number has no factors less than 104, am I right in assuming that this leaves a chance of about log(1028)/(2*log(104)) = 1:3.5, i.e. 28.57%, that this number will be prime?
By Merten's theorem, log(1028)/(1.781*log(104)) is a better approximation.

1.781 =e^gamma

2010-10-29, 17:31   #3
mart_r

Dec 2008
you know...around...

10011011002 Posts

Quote:
 Originally Posted by axn By Merten's theorem, log(1028)/(1.781*log(104)) is a better approximation. 1.781 =e^gamma
Oh! That would explain everything.
Thanks!

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