rogerfederer07's blog

By rogerfederer07, history, 3 years 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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3 years 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

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    9 months ago, # ^ |
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    Is there any way to find the maximum number of distinct prime factors of all the numbers in the range [1, N]?

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      9 months ago, # ^ |
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      Multiply first prime numbers while result is less than N.