%I #7 Mar 26 2019 19:20:34
%S 3,4,5,6,40
%N Numbers n such that n!^2-+8663 are primes.
%C Next term is larger than 72
%C a(6) > 1000 (if it exists) - _Robert Price_, Mar 26 2019
%t lst={};a=8663;Do[If[PrimeQ[n!^2-a]&&PrimeQ[n!^2+a],AppendTo[lst,n]],{n,3*4!}];lst
%Y Cf. A144046, A154660, A154661, A154662, A154663, A154664
%K nonn,more
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 13 2009