A186243 Numbers k such that 6*k-5 and 6*k-1 are both primes.

2, 3, 4, 7, 8, 12, 14, 17, 18, 19, 22, 28, 33, 38, 39, 47, 52, 53, 59, 64, 67, 74, 77, 78, 82, 84, 103, 108, 113, 124, 127, 129, 138, 143, 144, 147, 148, 152, 157, 162, 169, 182, 183, 203, 214, 217, 218, 238, 239, 242, 248, 249, 259, 262, 264, 267, 269

Offset: 1

Author

Jonathan Vos Post, Feb 15 2011

Keywords

• nonn
• easy
• changed

Comments

Numbers k such that 6*k-5 and 6*k-1 are cousin primes. The D = 2 numbers in class II, from page 3 of Weber. - Jonathan Vos Post, Feb 14 2011

Examples

			a(3) = 4 because 6*4-5 = 19 is prime, and 6*4-1 = 23 is prime.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• H. J. Weber, Exceptional Prime Number Twins, Triplets and Multiplets, arXiv:1102.3075 [math.NT], 2011.
• Eric W. Weisstein, Cousin Primes.

Crossrefs

Cf. A023200, A046132, A088765.

Programs

Mathematica

Select[Range[400], PrimeQ[6#-5] && PrimeQ[6#-1] &] (* Alonso del Arte, Feb 16 2011 *)

Formula

{k such that 6*k-5 is in A023200} = {k such that 6*k-1 is in A046132}.