[seqfan] Definite prime in A224848?
israel at math.ubc.ca
israel at math.ubc.ca
Sun Jan 15 21:53:49 CET 2023
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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