[seqfan] Re: Definite prime in A224848?

[Neil Sloane]

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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