A236509 Primes p with p + 2, p + 6 and prime(p) + 6 all prime.

5, 11, 107, 227, 311, 347, 821, 857, 1091, 1607, 1997, 2657, 3527, 4931, 5231, 8087, 8231, 9431, 10331, 11171, 12917, 13691, 13877, 21377, 22271, 24917, 27737, 29567, 32057, 33347, 35591, 36467, 37307, 39227, 42017

Offset: 1

Author

Zhi-Wei Sun, Jan 27 2014

Keywords

• nonn

Comments

According to the conjecture in A236508, this sequence should have infinitely many terms.

Examples

			a(1) = 5 since 5, 5 + 2 = 7, 5 + 6 = 11 and prime(5) + 6 = 17 are all prime, but 2 + 2 = 4 and 3 + 6 = 9 are both composite.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A022004, A023201, A046117, A236464, A236508.

Programs

Mathematica

p[n_]:=p[n]=PrimeQ[n+2]&&PrimeQ[n+6]&&PrimeQ[Prime[n]+6]
n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10^6}]