Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

What is the probability of $p_n$ being the greatest prime factor of a random number?

share|improve this question
Welcome to this site! May I ask what you mean by GPF? Is it Greatest Prime Factor? –  FrenzY DT. Nov 25 '12 at 11:27
What is a random number? As you may know, there is no such thing as a uniform distribution on the set of positive integers. Anyway, in some sense the answer is zero, since for any given $x$ the set of integers with no prime factor exceeding $x$ has density zero. –  Gerry Myerson Nov 25 '12 at 11:54
there is a "similar" answer to the probability of $p_n$ being the smallest prime factor $f(n)= (1-S(f(n-1)))/p(n)$ so i was wondering what could the probability for GPF –  John N Nov 25 '12 at 12:13

1 Answer 1

This can be determined by the Dickman function.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.