rogerfederer07's blog

By rogerfederer07, history, 5 weeks ago, In English

Is there any formula for calculating the count of prime factors of a number 'N'? I know the loose upper bound is log2(N) but is there a better upper bound? Thanks.

 
 
 
 
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5 weeks ago, # |
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There is no deterministic solution as of now, but it is a very famous fact that Hardy and Ramanujan proved that "for most numbers" (in the probabilistic sense), the number of distinct prime factors of a number $$$n$$$ is $$$log(log(n))$$$.

Hardy-Ramanujan Theorem