Quote:
Originally Posted by mart_r
Suppose I have an integer of magnitude of about 10^{28}.
If this number has no factors less than 10^{4}, am I right in assuming that this leaves a chance of about log(10^{28})/(2*log(10^{4})) = 1:3.5, i.e. 28.57%, that this number will be prime?

By Merten's theorem, log(10
^{28})/(
1.781*log(10
^{4})) is a better approximation.
1.781 =e^gamma