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%I #18 Sep 08 2022 08:45:10
%S 3,4,5,6,9,31,41,373,589,812,989,1115,1488,1864,1918,4412,4686,5821,
%T 13830
%N Numbers n such that (n!-2)/2 is a prime.
%e (4!-2)/2 = 11 is a prime.
%t Select[Range[0, 14000], PrimeQ[(#! - 2) / 2] &] (* _Vincenzo Librandi_, Feb 18 2015 *)
%o (PARI) xfactpk(n,k=2) = { for(x=2,n, y = (x!-k)/k; if(isprime(y),print1(x", ")) ) }
%o (Magma) [n: n in [1..600]| IsPrime((Factorial(n)-2) div 2)]; // _Vincenzo Librandi_, Feb 18 2015
%Y Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199, A139200, A139201, A139202, A139203, A139204, A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071
%K hard,more,nonn
%O 1,1
%A _Cino Hilliard_, May 18 2003
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
%E Edited by _T. D. Noe_, Oct 30 2008