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

1, 2, 4, 5, 8, 10

Offset

1,2

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

Links

Table of n, a(n) for n=1..6.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A100595, A100599, A100858.

Sequence in context: A277010 A101394 A095031 * A191535 A079537 A094591

Adjacent sequences: A100595 A100596 A100597 * A100599 A100600 A100601

Keyword

nonn,hard,more,less

Author

Jonathan Vos Post, Nov 30 2004

Extensions

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

Status

approved