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Old 2010-10-29, 16:47   #1
mart_r
 
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Default 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?
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Old 2010-10-29, 17:17   #2
axn
 
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Quote:
Originally Posted by mart_r View Post
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
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Old 2010-10-29, 17:31   #3
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Originally Posted by axn View Post
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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