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

[Charles Greathouse <crgreathouse@gmail.com>]

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

http://www.cecm.sfu.ca/Pseudoprimes/index-2-to-64.html

cites Jan Feitsma's website which can be found at

https://web.archive.org/web/20150107172624/http://www.janfeitsma.nl/math/psp2/index

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

https://www.cecm.sfu.ca/Pseudoprimes/psps-below-2-to-64.txt.bz2

(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 Of course, I am not saying that the information is no longer valid.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.