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A100600 Numbers k such that (prime(k)-1)! + prime(k)^6 is prime. 2

%I #11 Apr 10 2020 08:14:08

%S 3,4,29,32,133

%N Numbers k such that (prime(k)-1)! + prime(k)^6 is prime.

%C k = {3, 4, 29, 32, 133} yields primes p(n) = {5, 7, 109, 131, 751}. There are no more such k up to k=100. Computed in collaboration with _Ray Chandler_.

%C a(6) > 600. - _Jinyuan Wang_, Apr 10 2020

%F Numbers k such that (prime(k)-1)! + prime(k)^6 is prime, where prime(k) is the k-th prime.

%e a(1) = 3 because (prime(3)-1)! + prime(3)^6 = (5-1)! + 5^6 = 15649 is the smallest prime of that form.

%t lst={};Do[p=Prime[n];If[PrimeQ[(p-1)!+p^6], AppendTo[lst, n]], {n, 10^2}];lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 08 2008 *)

%Y Cf. A100599, A100602, A100858.

%K nonn,hard,more

%O 1,1

%A _Jonathan Vos Post_, Nov 30 2004

%E a(5) from _Jinyuan Wang_, Apr 10 2020

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