G. M.-S. on Mon, 08 Jul 2024 23:54:37 +0200


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Re: Are there known false positives for GP ispseudoprime() ?


Thanks, Charles.

Guillermo

On Mon, 8 Jul 2024 at 23:32, Charles Greathouse <crgreathouse@gmail.com> wrote:
Jan Feitsma, as I recall, has left academia. I think he originally intended to publish the result but never got around to it once he was in the professional world.

I didn't realize Galway had dropped off the 'net; not sure where he went.

In any case I agree that verification would be good. Feitsma's search was nontrivial and replicating it would be a good bit of work. With greater computer power available today, it might just be possible to brute-force it without use of delicate methods.

On Mon, Jul 8, 2024 at 2:32 PM G. M.-S. <lists.gms@gmail.com> wrote:

First of all, I am no specialist, so I may be wrong.

I have been unable to find anything recent about William Galway and Jan Feitsma and their past work.

The link
cites Jan Feitsma's website which can be found at
and has not been updated since 2013-04-02.
In particular, verification of the results does not seem to have been achieved.

So I wonder about the reliability of the file
(such an important result should be well documented, IMHO).
 
My 2 ¢.

Best,

Guillermo

On Mon, 8 Jul 2024 at 18:59, Bill Allombert <Bill.Allombert@math.u-bordeaux.fr> wrote:
On Mon, Jul 08, 2024 at 06:13:12PM +0200, G. M.-S. wrote:
> On Mon, 8 Jul 2024 at 14:51, Bill Allombert <
> Bill.Allombert@math.u-bordeaux.fr> wrote:
>
> >    There  are  no known composite numbers passing the above test,
> > although it is expected that infinitely many such numbers exist.   In
> >    particular,   all  composites  <= 2^{64} are correctly detected
> > (checked using
> >    http://www.cecm.sfu.ca/Pseudoprimes/index-2-to-64.html).
> >
> Just to say that this link is utterly obsolete, as are the 2 linked
> references mentioned in it.
> Of course, I am not saying that the information is no longer valid.

The link still provide psps-below-2-to-64.txt.bz2
which is all that matters.

Do you have a better link ?

Cheers,
BIll.