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

3, 4, 29, 32, 133

Offset: 1

Author

Jonathan Vos Post, Nov 30 2004

Keywords

• nonn
• hard
• more

Comments

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.

a(6) > 600. - Jinyuan Wang, Apr 10 2020

a(6) > 2500. - Michael S. Branicky, Jul 02 2024

Examples

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

Crossrefs

Cf. A100599, A100602, A100858.

Programs

Mathematica

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 *)

Formula

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

Extensions

a(5) from Jinyuan Wang, Apr 10 2020