[seqfan] Re: Definite prime in A224848?

[hv at crypt.org]

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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