A100602 Numbers k such that (prime(k)-1)! + prime(k)^5 is prime.

6, 8, 11, 17, 2286

Offset: 1

Author

Jonathan Vos Post, Nov 30 2004

Keywords

• nonn
• hard
• more

Comments

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.

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

Examples

			a(1) = 6 because (prime(6)-1)! + prime(6)^5 = (13-1)! + 13^5 = 479372893 is the first prime of this form.
		

Crossrefs

Cf. A100600, A100858.

Programs

Mathematica

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 *)

PARI

is(k) = ispseudoprime((prime(k)-1)! + prime(k)^5); \\ Jinyuan Wang, Apr 10 2020

Formula

Numbers k such that (prime(k)-1)! + prime(k)^5 is prime, where prime(k) is the k-th prime.

Extensions

a(5) from Michael S. Branicky, Jul 02 2024