hermann on Thu, 28 Aug 2025 13:49:00 +0200


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PARI/GP wrong on 7!!+7+1 being not prime, or oeis.org/Mathematica? 

The sequence is:
https://oeis.org/search?q=5%2c7%2c13%2c113%20id:A118743
Bottom output for n up to 250 is returned immediately, for up to 1250 takes 3 seconds. 

On fast AMD 7950X CPU with 5.6GHz boost frequency up to 12 takes minutes
But more importantly, 7!!+7+1 is not reported as prime.
Is 7!!+7+1 prime or not?

hermann@7950x:~$ gp -q
? for(n=1,12,if(isprime(n!!+n+1),print(n,": ",n!!+n+1));print1("."))
1: 3
.2: 5
...........
? ##
  ***   last result computed in 4min, 32,167 ms.
?


Regards,

Hermann.

pi@raspberrypi5:~ $ wolframscript
Wolfram Language 14.2.1 Engine for Linux ARM (64-bit)
Copyright 1988-2025 Wolfram Research, Inc.

In[1]:= Select[Table[n!!+n+1, {n, 250}], PrimeQ]

Out[1]= {3, 5, 7, 13, 113, 3851, 46093, 10321937, 185794579,


   216862434431944426122117120047,
1874480713189654839282450157086195210900931486780353469173376681742503659\
434414632312033372643386765197475111737132341321962070865661132800000000\ 


    000000000173}


In[2]:=