A046137 Primes p such that p+4 and p+12 are also prime.

7, 19, 67, 97, 127, 229, 397, 487, 739, 757, 907, 1009, 1279, 1447, 1567, 1597, 1609, 1867, 1999, 2239, 2269, 2377, 2539, 2659, 2707, 3037, 3217, 3319, 3457, 3529, 3697, 3877, 3907, 3919, 4639, 4789, 4999, 5167, 5437, 5569, 5647, 5689, 5737

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

All terms == 1 (mod 6). - Robert Israel, Jul 24 2015

Links

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

Programs

Maple

select(t -> isprime(t) and isprime(t+4) and isprime(t+12), [6*i+1 $ i=1..1000]); # Robert Israel, Jul 24 2015

Mathematica

Select[Range@ 5760, AllTrue[{#, # + 4, # + 12}, PrimeQ] &] (* Michael De Vlieger, Jul 24 2015, Version 10 *)
Select[Prime[Range[800]],AllTrue[#+{4,12},PrimeQ]&] (* Harvey P. Dale, Apr 18 2022 *)

PARI

lista(nn) = forprime(p=2, nn, if (isprime(p+4) && isprime(p+12), print1(p, ", "))); \\ Michel Marcus, Jul 24 2015

Formula

A023200 INTERSECT A046133. - R. J. Mathar, Jan 23 2009