I get 13% less primes than I expected:-(

[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?

[axn]

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

[mart_r]

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!