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- - **Expected Number of Factors for numbers within a ra**
(*https://www.mersenneforum.org/showthread.php?t=9752*)

Expected Number of Factors for numbers within a raHello,
I was wondering if there's a simple formula to estimate the number of prime factors for a number in some range say a to b. For instance, between x=900 and x=1000, the expected number of prime factors is 3.04 ~ 3. |

It's very well known that the expected number of different prime factors for a large positive integer N is log(log(N))+O(1), this is also true if you write multiplicity instead of different. So the answer is also log(log(b))+O(1) for your question, supposing that b is large and a isn't very close to b.
You can prove this using Merten's theorem: sumprime(p=2,n,1/p)=log(log(n))+O(1) is enough for you. |

Heh, not well enough I guess.
Thanks |

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