11202Re: [PrimeNumbers] Fw: Time (lg n)^(4+o(1)) for randomized primality proving
- Jan 30, 2003--- Yves Gallot <galloty@...> wrote:
> Did someone read it?OK, it looks like it's a somewhat novel interpretation of the word
> Is it theoretically fast and/or practically fast?
'certificate', with certificate finding taking O(d^(2+o(1))), and
verification taking O(d^(4+o(1))). (d=ln(n))
Using that definition, APRCL and BLS have a certificate - a list of
all the things you need to compute (and that take all the time).
I looked at his verification claims, and to be honest I've rarely seen so
many o(1)s. Given the slow growth of the third log in the APRCL exponent,
and the already-seen following of the predicted growth, I reckon that he's
going to have to look a long way to get those o(1)s to become negligible.
(The axes are cryptic (but log/log) at http://fatphil.org/maths/APRCL/
where there's a chart of some tests I did just last month, and the gradient
is clear. I will have some >1000 digit values added to that chart soon).
His own wording makes it sound as if he thinks that it will become faster
than APRCL and ECPP for a real example. The fact that he's sitting on his
optimisations means that it's too soon to judge. You must remember that
Professor Bernstein is not just a theoriser, but also an implementer, and a
darned good one at that, so I'm hoping that he will support his own
predictions with real figures.
Is that free as in Willy or as in bird?
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