A046138 Primes p such that p+6 and p+8 are also primes.

5, 11, 23, 53, 101, 131, 173, 191, 233, 263, 563, 593, 653, 821, 1013, 1223, 1283, 1481, 1601, 1613, 1871, 2081, 2333, 2543, 2963, 3251, 3323, 3461, 3533, 3761, 3911, 3923, 4013, 4211, 4253, 4643, 4793, 5003, 5273, 5471, 5651, 5843, 5861, 6263, 6353, 6563

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Links

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

Crossrefs

Cf. A023201, A023202.

Programs

Magma

[p: p in PrimesUpTo(10^4)| IsPrime(p+6) and IsPrime(p+8)]; // Vincenzo Librandi, Jul 26 2015

Maple

for a from 3 by 2 to 10000 do
if `and`(isprime(a), isprime(a+6), isprime(a+8)) then print(a); end if;
end do; # Matt C. Anderson, Jul 24 2015

Mathematica

Select[Range@ 6000, AllTrue[{#, # + 6, # + 8}, PrimeQ] &] (* Michael De Vlieger, Jul 24 2015, Version 10 *)
Select[Prime[Range[1000]],AllTrue[#+{6,8},PrimeQ]&] (* Harvey P. Dale, Jun 05 2024 *)

Perl

use ntheory ":all"; say for sieve_prime_cluster(0,1e5, 6,8); # Dana Jacobsen, Oct 17 2017

Formula

A023201 INTERSECT A023202. - R. J. Mathar, Jan 23 2009