Rather than downvoting you to oblivion, I'll point out that "Restricting the problem to a fixed size input makes factoring an O(1) operation" makes no sense. So

Rather than downvoting you to oblivion, I'll point out that "Restricting the problem to a fixed size input makes factoring an O(1) operation" makes no sense. Sorting an array of N items using a comparison sort has a lower complexity bound of O(N log(N)) in the worst case. Yes, of course that becomes O(1) if you say N is constant, but that's really not helpful at all.