A078946 Primes p such that p, p+2, p+6, p+12 and p+14 are consecutive primes.

17, 227, 1277, 1607, 3527, 3917, 4637, 4787, 27737, 38447, 39227, 44267, 71327, 97367, 99707, 113147, 122027, 122387, 124337, 165707, 183497, 187127, 191447, 197957, 198827, 275447, 290657, 312197, 317957, 347057, 349397, 416387, 418337, 421697, 427067, 443867

Offset: 1

Author

Labos Elemer, Dec 19 2002

Keywords

• nonn

Examples

			227 is in the sequence since 227, 229 = 227 + 2, 233 = 227 + 6, 239 = 227 + 12 and 241 = 227 + 14 are consecutive primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
• Eric Weisstein's World of Mathematics, Prime Triplet.

Crossrefs

Subsequence of A128468.

Subsequence of A078847. - R. J. Mathar, Feb 10 2013

Cf. A001223, A078866, A078867, A078947-A078971, A022006, A022007.

Programs

Magma

[p: p in PrimesInInterval(7,1000000) | forall{i: i in [2,6,12,14] | IsPrime(p+i)}]; // Vincenzo Librandi, Apr 19 2015

Mathematica

Rest@ Select[Prime@ Range@ 36000, AllTrue[{2, 6, 12, 14} + #, PrimeQ] &] (* Michael De Vlieger, Apr 18 2015, Version 10 *)
Select[Partition[Prime[Range[36000]],5,1],Differences[#]=={2,4,6,2}&][[All,1]] (* Harvey P. Dale, Jun 14 2022 *)

PARI

isok(p) = isprime(p) && (nextprime(p+1)==p+2) && (nextprime(p+3)== p+6) && (nextprime(p+7)==p+12) && (nextprime(p+13)==p+14); \\ Michel Marcus, Dec 10 2013

PARI

list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 2 && p3 - p2 == 4 && p4 - p3 == 6 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Formula

a(n) == 17 (mod 30). - Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002