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

6, 8, 11, 17, 2286

Offset

1,1

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

Links

Table of n, a(n) for n=1..5.

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A100600, A100858.

Sequence in context: A048586 A080824 A183979 * A222175 A350767 A315856

Adjacent sequences: A100599 A100600 A100601 * A100603 A100604 A100605

Keyword

nonn,hard,more

Author

Jonathan Vos Post, Nov 30 2004

Extensions

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

Status

approved