A051453 Prime powers such that 1 + lcm(1,2,...,p^w) is prime.

1, 2, 3, 4, 5, 7, 9, 19, 25, 31, 47, 89, 127, 139, 1369, 2251, 3271, 4253, 4373, 4549, 5449, 13331, 37123, 55291, 79633, 105653

Offset: 1

Author

Labos Elemer

Keywords

• nonn
• more

Examples

			1 + lcm(1,2,..,89) = 718766754945489455304472257065075294401 is prime.
		

Crossrefs

Cf. A000961, A003418, A049536, A049537.

Programs

PARI

ispp(n) = isprimepower(n) || n==1;
lista(nn) = {for (n=1, nn, if (ispp(n) && ispseudoprime(1+lcm([1..n])), print1(n, ", ")););} \\ Michel Marcus, Aug 26 2019

Extensions

Corrected and extended by Wouter Meeussen, Apr 18 2003

a(18)-a(22) from Jinyuan Wang, May 02 2020

a(23)-a(24) from Michael S. Branicky, Apr 22 2023

a(25)-a(26) from Michael S. Branicky, Jul 04 2025