A100599 Numbers k such that (prime(k)-1)! + prime(k)^7 is prime.

7, 14, 16, 59

Offset: 1

Author

Jonathan Vos Post, Nov 30 2004

Keywords

• nonn
• hard
• more

Comments

k = {7, 14, 16, 59} yields primes p(k) = {17, 43, 53, 277}. There are no more such k up to k=100. Computed in collaboration with Ray Chandler.

a(5) > 600. - Jinyuan Wang, Apr 10 2020

a(5) > 2500. - Michael S. Branicky, Jul 02 2024

Examples

			a(1) = 7 because (prime(7)-1)! + prime(7)^7 = (17-1)! + 17^7 = 20923200226673 is the smallest prime of that form.
		

Crossrefs

Cf. A100598, A100600, A100858.

Programs

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[(p-1)!+p^7], AppendTo[lst, n]], {n, 10^2}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)

PARI

is(k) = ispseudoprime((prime(k)-1)! + prime(k)^7); \\ Jinyuan Wang, Apr 10 2020