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Looking for O (n^(1/3)) factoring algorithm
Posted:
Jan 18, 2013 4:34 PM


Some years ago I found a factoring algorithm on the internet that worked in O (n^(1/3)) worst case and was reasonably easy to understand for mere mortals. Invented sometime around 1975. The principle was using Fermat's algorithm which finds factors of almost equal size quickly, then extending it to find factors with a ratio p/q for small p and q, and cleverly arranging things so that every factor is guaranteed to be found in O (N^(1/3)) (and not finding any factors proves primality). Lost the paper, and can't remember the name of the author or any other detail.
Can anyone help? Not interested in any faster algorithms that are hard to understand; this was apparently the first method found that was faster than wellimplemented trial division, didn't involve any particularly difficult maths, and is probably not in use anymore.



