A023241 Primes that remain prime through 2 iterations of function f(x) = x + 6.

5, 7, 11, 17, 31, 41, 47, 61, 67, 97, 101, 151, 167, 227, 251, 257, 271, 347, 367, 557, 587, 601, 607, 641, 647, 727, 941, 971, 1091, 1097, 1117, 1181, 1217, 1277, 1291, 1361, 1427, 1447, 1481, 1487, 1601, 1607, 1657, 1741, 1747, 1777, 1861, 1867, 1901, 1987

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that p+6 and p+12 are also primes.

Links

• Lei Zhou, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Prime Triplet

Programs

Magma

[n: n in [0..1000] | IsPrime(n) and IsPrime(n+6) and IsPrime(n+12)] // Vincenzo Librandi, Nov 20 2010

Mathematica

triq[p_] := And[PrimeQ[p + 6], PrimeQ[p + 12]]; Select[Prime[Range[1000]], triq]  (* Ben Branman, Sep 03 2012 *)
nrpQ[n_]:=AllTrue[Rest[NestList[#+6&,n,2]],PrimeQ]; Select[Prime[Range[ 300]],nrpQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 27 2021 *)