A051648 Primes of form 210*p + 1 where p is a prime.

421, 631, 1051, 1471, 2311, 2731, 3571, 4831, 6091, 9871, 11131, 12391, 14071, 15331, 17431, 18691, 21211, 28771, 29191, 32971, 34231, 37591, 38011, 40111, 40531, 46831, 48091, 52711, 56911, 58171, 59011, 65731, 66571, 72871, 73291, 74131, 75391, 84211, 87991

Offset: 1

Author

Labos Elemer

Keywords

• nonn
• easy

Comments

Generalization of A005385. Can be called 210-safe primes.

A002110(4)*p + 1 = 210*p + 1 (prime).

Examples

			631 is in the sequence because 631 = 210*p + 1, where p=3.
		

Links

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

Crossrefs

Cf. A005384, A005385, A007693, A002110.

Programs

Mathematica

Select[Table[210n+1,{n,Prime[Range[100]]}],PrimeQ] (* Harvey P. Dale, Dec 25 2016 *)

PARI

isok(k) = isprime(k) && k % 210 == 1 && isprime((k-1)/210); \\ Amiram Eldar, Feb 24 2025

Formula

a(n) = 210 * A051647(n) + 1. - Amiram Eldar, Feb 24 2025