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%I #15 Jul 02 2024 14:18:59
%S 6,8,11,17,2286
%N Numbers k such that (prime(k)-1)! + prime(k)^5 is prime.
%C k = {6, 8, 11, 17} yields primes p(k) = {13, 19, 31, 59}. There are no more such k up to k=100. Computed in collaboration with _Ray Chandler_.
%C a(5) > 600. - _Jinyuan Wang_, Apr 10 2020
%F Numbers k such that (prime(k)-1)! + prime(k)^5 is prime, where prime(k) is the k-th prime.
%e a(1) = 6 because (prime(6)-1)! + prime(6)^5 = (13-1)! + 13^5 = 479372893 is the first prime of this form.
%t lst={};Do[p=Prime[n];If[PrimeQ[(p-1)!+p^5], AppendTo[lst, n]], {n, 10^2}];lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 08 2008 *)
%o (PARI) is(k) = ispseudoprime((prime(k)-1)! + prime(k)^5); \\ _Jinyuan Wang_, Apr 10 2020
%Y Cf. A100600, A100858.
%K nonn,hard,more
%O 1,1
%A _Jonathan Vos Post_, Nov 30 2004
%E a(5) from _Michael S. Branicky_, Jul 02 2024