I am currently working to understand Dixon's running time proof of his subexp integer factorization algorithm (random squares).
But unfortunately I can not follow him at a certain point in his work. His work is available for free here: http://www.ams.org/journals/mcom/1981-36-153/S0025-5718-1981-0595059-1/home.html
My problem occurs on the last page (page 6 of file, named page 260) where he states that in case of success the execution of step 1 is bound by 4hv+2, where h is the number of primes smaller v, and v is a fixed integer depending on n (the number we want to factorize). I really do not have a clue where this bound comes from. It might have to do something with the expected values of some steps in the algorithms, but these bound seems not probalistic as far as I unterstand him.
I guess this problem might only be comprehensible when you already read the whole paper. I am hoping to fluke here.
Best regards! Robert