A051651 Primes of the form 30030*p + 1 where p is a prime.

150151, 330331, 390391, 870871, 930931, 1231231, 1411411, 1831831, 2012011, 2372371, 2672671, 3813811, 4174171, 4474471, 5375371, 5435431, 5735731, 5915911, 8078071, 9219211, 10120111, 10420411, 11021011, 11501491, 12642631, 14024011, 14624611, 16246231, 16426411

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

Generalization of A005385; can be called 30030-safe primes.

A002110(6)*p + 1 = 30030*p + 1 (prime).

Examples

			390391 is a term because 390391 = 2*3*5*7*11*13*p + 1 is prime, where p = 13.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A005384, A005385, A007693, A051654.

Programs

Mathematica

Select[30030Prime[Range[100]]+1,PrimeQ] (* Harvey P. Dale, Dec 09 2010 *)

PARI

isok(k) = isprime(k) && k % 30030 == 1 && isprime((k-1)/30030); \\ Amiram Eldar, Feb 24 2025

Formula

a(n) = 30030 * A051654(n) + 1. - Amiram Eldar, Feb 24 2025