Quote:
Originally Posted by Till
nesio,
in fact we believe that Hart_Fast and Lehman_CustomKOrder are pretty fast.
If you have something better then just show it. Your SM pseudocode will hardly be it. The minimal improvement in iterations of RM is not impressive either.
Some comments on your points:
1. We do that in our implementations but did not in Hard_Nesio, because it is not in the SM pseudocode.

That was because we took Hart as is (we wrote above).
Quote:
2. I demonstrated with my performance test that this is not helpful. 10080 seems to be the best multiplier for any n if you store the sqrt's.

We meant flexible way (not constant).
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3. We did understand that.
4. What do you mean with "fast multiplication", replace it with iterated addition? This makes hardly a difference in Java. Maybe the compiler is doing that for us.
5. That might be interesting.
6. Which one's?

See
[1] R. Lehman, ‘Factoring Large Integers’. Mathematics of Computation, Volume 28, Number 126, April 1974, Pages 637646.
[2] Hart, William B. ‘A one line factoring algorithm’, 2012. Journal of the Australian Mathematical Society, Volume 92 (Number 1), Pages 6169.