A022012 Initial members of prime octuplets (p, p+2, p+6, p+12, p+14, p+20, p+24, p+26).

17, 1277, 113147, 2580647, 20737877, 58208387, 73373537, 76170527, 100658627, 134764997, 137943347, 165531257, 171958667, 224008217, 252277007, 294536147, 309740987, 311725847, 364154027, 408936947, 515447747, 521481197, 528272177, 619010297, 626927447, 682809977

Offset: 1

Author

Warut Roonguthai

Keywords

• nonn

Comments

All terms are congruent to 17 (modulo 30). - Matt C. Anderson, May 26 2015

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..10000 (first 1000 terms from Matt C. Anderson)
• T. Forbes and Norman Luhn, Prime k-tuplets
• Norman Luhn and Hugo Pfoertner, 10 million terms of A022012, 7z compressed (46.4 MB) (2021).

Crossrefs

A065706 is the union of A022011, A022012 and A022013.

A346997(n) = a(10^n).

Cf. A347850, A347851.

Programs

Magma

[p: p in PrimesUpTo(4*10^8) | forall{p+r: r in [2,6,12,14,20,24,26] | IsPrime(p+r)}]; // Vincenzo Librandi, Oct 01 2015

Mathematica

Select[Prime[Range[2 10^9]], Union[PrimeQ[# + {2, 6, 12, 14, 20, 24, 26}]] == {True} &] (* Vincenzo Librandi, Oct 01 2015 *)

PARI

forprime(p=2, 10^30, if (isprime(p+2) && isprime(p+6) && isprime(p+12) && isprime(p+14) && isprime(p+20) && isprime(p+24) && isprime(p+26), print1(p", "))) \\ Altug Alkan, Oct 01 2015

Perl

use ntheory ":all"; say for sieve_prime_cluster(1,1e10, 2,6,12,14,20,24,26); # Dana Jacobsen, Sep 30 2015