A100604 Numbers k such that (prime(k)-1)! + prime(k)^3 is prime.

2, 3, 4, 28, 894

Offset: 1

Author

Jonathan Vos Post, Nov 30 2004

Keywords

• nonn
• hard
• more

Comments

k = {2, 3, 4, 28} yields primes p(k) = {3, 5, 7, 107}. There are no more such k up to k=100. Verified by Ray Chandler.

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

a(6) > 2500. - Michael S. Branicky, Jul 02 2024

Examples

			a(3) = 4 because (prime(4)-1)! + prime(4)^3 = (7-1)! + 7^3 = 720 + 343 = 1063 is the 3rd prime of this form.
		

Crossrefs

Cf. A100605, A100858.

Programs

Mathematica

Select[Range[30],PrimeQ[(Prime[#]-1)!+Prime[#]^3]&] (* Harvey P. Dale, Jul 13 2022 *)

PARI

is(k) = ispseudoprime((prime(k)-1)! + prime(k)^3); \\ Jinyuan Wang, Apr 10 2020

Formula

Numbers k such that (prime(k)-1)! + prime(k)^3 is prime, where prime(k) is the k-th prime.

Extensions

a(5) from Michael S. Branicky, Jul 01 2024