A100598 Numbers k such that (prime(k)-1)! + prime(k)^8 is prime.

1, 2, 4, 5, 8, 10

Offset: 1

Author

Jonathan Vos Post, Nov 30 2004

Keywords

• nonn
• hard
• more
• less

Comments

k = {1, 2, 4, 5, 8, 10} yields primes p(k) = {2, 3, 7, 11, 19, 29}. There are no more such k up to k=100. Computed in collaboration with Ray Chandler.

a(7) > 600. - Jinyuan Wang, Apr 10 2020

a(7) > 900. - Tyler NeSmith, May 05 2021

a(7) > 2500. - Michael S. Branicky, Jul 03 2024

Examples

			a(1) = 1 because (prime(1)-1)! + prime(1)^8 = (2-1)! + 2^8 = 257 is the smallest prime of that form.
a(5) = 8 because (prime(8)-1)! + prime(8)^8 = (19-1)! + 19^8 = 304888344611713861001750412961 is the 5th smallest prime of that form.
		

Crossrefs

Cf. A100595, A100599, A100858.

Programs

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[(p-1)!+p^8], AppendTo[lst, n]], {n, 10^2}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)

PARI

is(k) = ispseudoprime((prime(k)-1)! + prime(k)^8); \\ Jinyuan Wang, Apr 10 2020

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 08 2007