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Topic: Looking for O (n^(1/3)) factoring algorithm
Replies: 3   Last Post: Jan 19, 2013 9:18 AM

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gnasher729

Posts: 418
Registered: 10/7/06
Looking for O (n^(1/3)) factoring algorithm
Posted: Jan 18, 2013 4:34 PM
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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 well-implemented trial division, didn't involve any
particularly difficult maths, and is probably not in use anymore.



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