A100603 Numbers k such that (prime(k)-1)! + prime(k)^4 is prime.

1, 2, 4, 67, 212, 1615, 2570

Offset

1,2

Comments

k = {1, 2, 4, 67} yields primes p(k) = {2, 3, 7, 331}. There are no more such k up to k=100. Computed in collaboration with Ray Chandler.

Terms a(5) and greater are only probable primes. - Iain Fox, Mar 05 2018

Links

Table of n, a(n) for n=1..7.

Formula

Numbers k such that (prime(k)-1)! + prime(k)^4 is prime, where prime(k) is the k-th prime.

Example

a(3) = 4 because (prime(4)-1)! + prime(4)^4 = (7-1)! + 7^4 = 720 + 2401 = 3121 is the 3rd prime of this form.

Mathematica

lst={}; Do[p=Prime[n]; If[PrimeQ[(p-1)!+p^4], AppendTo[lst, n]], {n, 10^2}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)

Prog

(PARI) is(k) = my(p=prime(k)); ispseudoprime((p-1)! + p^4) \\ Iain Fox, Mar 05 2018

Crossrefs

Cf. A100858.

Sequence in context: A279969 A361228 A018364 * A374235 A362456 A301818

Adjacent sequences: A100600 A100601 A100602 * A100604 A100605 A100606

Keyword

nonn,more

Author

Jonathan Vos Post, Nov 30 2004

Extensions

a(5) from Iain Fox, Mar 05 2018

a(6) from Iain Fox, Mar 11 2018

a(7) from Michael S. Branicky, May 29 2025

Status

approved