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

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

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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