A100600 -id:A100600 - cp's OEIS frontend

A100599 Numbers k such that (prime(k)-1)! + prime(k)^7 is prime.

7, 14, 16, 59

Offset: 1

Jonathan Vos Post, Nov 30 2004

k = {7, 14, 16, 59} yields primes p(k) = {17, 43, 53, 277}. There are no more such k up to k=100. Computed in collaboration with Ray Chandler.
a(5) > 600. - Jinyuan Wang, Apr 10 2020
a(5) > 2500. - Michael S. Branicky, Jul 02 2024

			a(1) = 7 because (prime(7)-1)! + prime(7)^7 = (17-1)! + 17^7 = 20923200226673 is the smallest prime of that form.

Cf. A100598, A100600, A100858.

lst={};Do[p=Prime[n];If[PrimeQ[(p-1)!+p^7], AppendTo[lst, n]], {n, 10^2}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)

is(k) = ispseudoprime((prime(k)-1)! + prime(k)^7); \\ Jinyuan Wang, Apr 10 2020

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

Original entry on oeis.org

6, 8, 11, 17, 2286

Offset: 1

Jonathan Vos Post, Nov 30 2004

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

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

Cf. A100600, A100858.

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 *)

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

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

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

cp's OEIS Frontend

A100599 Numbers k such that (prime(k)-1)! + prime(k)^7 is prime.

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