A164566 Primes p such that 7*p-6 and 7*p+6 are also prime numbers.

5, 11, 19, 31, 41, 61, 71, 109, 151, 211, 229, 269, 379, 419, 431, 439, 479, 619, 641, 709, 739, 809, 839, 971, 1009, 1069, 1229, 1259, 1319, 1361, 1439, 1451, 1499, 1531, 1579, 1669, 1801, 1879, 1889, 2011, 2111, 2239, 2269, 2381, 2411, 2551, 2579, 2591

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Keywords

• nonn
• easy

Comments

Primes of the form A087681(k)/7, any index k.

Examples

			For p=5, both 7*5-6=29 and 7*5+6=41 are prime,
for p=11, both 7*11-6=71 and 7*11+6=83 are prime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A106015, A125272, A127430, A046133, A087681, A136052, A023225.

Programs

Magma

[p: p in PrimesUpTo(3000) | IsPrime(7*p-6) and IsPrime(7*p+6)]; // Vincenzo Librandi, Apr 09 2013

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[7*p-6]&&PrimeQ[7*p+6],AppendTo[lst,p]], {n,6!}];lst
Select[Prime[Range[700]], And @@ PrimeQ/@{7 # + 6, 7 # - 6}&] (* Vincenzo Librandi, Apr 09 2013 *)

PARI

is(n)=isprime(n) && isprime(7*n-6) && isprime(7*n+6) \\ Charles R Greathouse IV, Mar 28 2017

Formula

A136052 INTERSECT A023225. [R. J. Mathar, Aug 20 2009]

Extensions

Examples rephrased by R. J. Mathar, Aug 20 2009