[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


More information about the SeqFan mailing list