A347851 -id:A347851 - cp's OEIS frontend

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

Warut Roonguthai

nonn

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

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).

A065706 is the union of A022011, A022012 and A022013.
A346997(n) = a(10^n).
Cf. A347850, A347851.

[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

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

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

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

A347850 Record gaps between prime octuplets of the form p + {0, 2, 6, 12, 14, 20, 24, 26} (initial members are A022012), divided by 30.

Original entry on oeis.org

42, 3729, 82250, 605241, 1249017, 1734985, 1747606, 3550360, 9578800, 10562911, 12208504, 24101070, 26510262, 38121281, 38588851, 47884158, 50246371, 56392908, 59827439, 66233760, 114058040, 120197366, 141646351, 141808504, 153247005, 168751151, 235079194, 244505074

Offset: 1

Hugo Pfoertner and Norman Luhn, Sep 16 2021

nonn

			a(1) = (A022012(2) - A022012(1))/30 = (1277 - 17)/30 = 42; 17 = A347851(1).
a(5) = (A022012(13) - A022012(12))/30 = (171958667 - 165531257)/30 = 214247, exceeding all previous differences; 1655531257 = A347851(5).

Norman Luhn, Table of n, a(n) for n = 1..79
Norman Luhn, The "Smallest prime k-tuplets" database.
Norman Luhn, Record Gaps Between Prime Octuplets.

The primes at the lower end of the record gaps are given in A347851.

Cf. A022012, A346997, A347848, A347852.

cp's OEIS Frontend

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

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