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%I
%S 2,3,7,41,757
%N Primes of the form n! + n^2 + 1.
%C Primes of the form A004664(n) + 1. For n! + n^2 + 1 to be prime, n>1, it is necessary but not sufficient for n to be even. 74! + 74^2 + 1 is composite, with 108 digits; the next possible prime of the form n! + n^2 + 1 has n>75.
%C No more terms for n<1150. [From V. Librandi, Dec 22 2010]
%F A000040 INTERSECTION {n! + n^2 + 1}.
%t lst={};Do[s=n!+n^2;If[PrimeQ[p=s+1], AppendTo[lst, p]], {n, 0, 5!}];lst [From _Vladimir Joseph Stephan Orlovsky_, Sep 27 2008]
%o (MAGMA) [ a: n in [0..1150] | IsPrime(a) where a is Factorial(n)+n^2+1 ]; [From Vincenzo Librandi, Dec 22 2010]
%Y Cf. A000040, A004664, A119448.
%K nonn,less
%O 1,1
%A _Jonathan Vos Post_, Jul 28 2006
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