A051644 Primes of the form 6*p + 1 where p is also prime.

13, 19, 31, 43, 67, 79, 103, 139, 223, 283, 367, 439, 499, 607, 619, 643, 787, 823, 907, 1039, 1087, 1399, 1447, 1543, 1579, 1627, 1663, 1699, 1759, 1867, 1879, 1987, 2083, 2203, 2239, 2383, 2659, 2767, 2803, 3019, 3343, 3463, 3559, 3607, 3643, 3847, 3919

Offset: 1

Author

Labos Elemer

Keywords

• nonn
• easy

Comments

Analogous to A005385; can be called 6-safe primes.

Examples

			103 is in the sequence because both 17 and 6*17 + 1 = 103 are primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)

Crossrefs

Cf. A005384, A005385, A002476, A007693, A016921, A024899, A091178.

Programs

Mathematica

Select[1 + 6Prime@Range[120], PrimeQ] (* Ray Chandler, Mar 14 2007 *)

PARI

isok(k) = isprime(k) && k % 6 == 1 && isprime((k-1)/6); \\ Amiram Eldar, Feb 24 2025

Formula

a(n) = 6*A007693(n) + 1.

Extensions

Edited, corrected and extended by Ray Chandler, Mar 14 2007