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%I
%S 2,5,17,109
%N Primes of the form n!+n^3+n^2+n+1.
%C The associated n are 0,1,2,4,... (and no further between 4 and 2020, ie., the next prime has at least 5802 digits).
%t lst={};Do[p=n!+n^3+n^2+n+1;If[PrimeQ[p],AppendTo[lst,p]],{n,0,6!}];lst
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jun 14 2009