I have recently decided to read up on the current integer factorization algorithms. When looking into some of the algorithms, I came across the following statement:
Say that p is the smallest prime factor of n. By Dixon's Theorem, the probability that the largest factor of n is less than $(p)^\epsilon$ is roughly $\epsilon ^ {- \epsilon}$.
But when I hear Dixon's Theorem, I think of this. I currently don't see how Dixon's Theorem yields such a probabilistic bound. Can you help me with that?
And the disclaimer - I am not currently in any class, so this was not assigned to me, it is not a homework problem, and I will in no way be receiving any sort of academic credit for this work.