[seqfan] Re: Definite prime in A224848?

[Sean A. Irvine]

Done.

On Tue, 17 Jan 2023 at 03:20, Neil Sloane <njasloane at gmail.com> wrote:

> I wrote to Kellen yesterday, but he has not replied.  I propose that we
> assume that no certificate exists.  Can someone make the necessary edits?
> Say "probable prime".
>
> Best regards
> Neil
>
> Neil J. A. Sloane, Chairman, OEIS Foundation.
> Also Visiting Scientist, Math. Dept., Rutgers University,
> Email: njasloane at gmail.com
>
>
>
> On Mon, Jan 16, 2023 at 7:47 AM <hv at crypt.org> wrote:
>
> > For an assertion that a 18269-digit number is prime, I would want to see
> > a primality certificate; without one, I would definitely consider that
> > assertion dubious.
> >
> > I would guess that Kellen Myers has not generated such a certificate,
> > or they would not have needed to check both Mathematica and Maple.
> >
> > (The history appears to say that Kellen self-approved the edit, am
> > I reading that correctly?)
> >
> > Hugo
> >
> > israel at math.ubc.ca wrote:
> > :A224848 has the Comments:
> > :
> > :The number corresponding to a(5) = 2818 is a probable prime of 18269
> > :digits. - Giovanni Resta, Jul 25 2013
> > :
> > :The number corresponding to a(5) = 2818 is prime (definite, not
> > probable),
> > :according to Wolfram Mathematica 11.0 and Maple 2018. - Kellen Myers,
> Dec
> > :04 2019
> > :
> > :At least as far as Maple 2018 is concerned, I doubt that Kellen's
> comment
> > :is correct. Maple's "isprime" command is (and has always been, as far as
> > I
> > :know) a probabilistic primality tester. The help page for it says
> > :------------- It returns false if n is shown to be composite within one
> > :strong pseudo-primality test and one Lucas test. It returns true
> > otherwise.
> > :If isprime returns true, n is very probably prime - see References
> > section.
> > :No counterexample is known and it has been conjectured that such a
> > counter
> > :example must be hundreds of digits long. -------------
> > :
> > :I'm not sure about Mathematica 11.0, but last I heard Mathematica's
> > :"PrimeQ" was also using a probabilistic test. Or is Kellen referring to
> > :deterministic tests implemented in Mathematica and Maple, rather than
> > :"isprime" and "PrimeQ"?
> > :
> > :Cheers,
> > :Robert
> > :
> > :--
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> >
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