A257168 Numbers n such that n, n+2, n+8, n+14, n+18, n+20, n+24, n+30, n+32, n+38, n+42, n+44, n+48 and n+50 are all prime.

79287805466244209, 2714623996387988519, 5012524663381750349, 6120794469172998449, 6195991854028811669, 6232932509314786109, 6808488664768715759, 10756418345074847279, 11319107721272355839, 12635619305675250719, 14028155447337025829, 14094050870111867489, 14603617704434643719, 14777669568340323479, 15420967329931107779, 16222575536498135639, 16624441191356313149, 17367037621075657349, 19289576760019250519

Offset: 1

Author

Tim Johannes Ohrtmann, Apr 17 2015

Keywords

• nonn

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..209 [first 75 terms computed by Betsis and Säfholm, Forbes, Vlesycit, and Waldvogel (1982-2009)]
• Tony Forbes and Norman Luhn, Smallest Prime k-tuplets
• Norman Luhn, Table of n, a(n) for n = 1..891 (up to 10^22).

Crossrefs

Initial members of all of the first prime k-tuplets:

twin primes: A001359.

prime triples: A007529 out of A022004, A022005.

prime quadruplets: A007530.

prime 5-tuples: A086140 out of A022007, A022006.

prime sextuplets: A022008.

prime septuplets: A257124 out of A022009, A022010.

prime octuplets: A065706 out of A022011, A022012, A022013.

prime nonuplets: A257125 out of A022547, A022548, A022545, A022546.

prime decaplets: A257127 out of A027569, A027570.

prime 11-tuplets: A257129 out of A213646, A213647.

prime 12-tuplets: A257131 out of A213601, A213645.

prime 13-tuplets: A257135 out of A214947, A257137, A257138, A257139, A257140, A257141.

prime 14-tuplets: A257166 out of A257167, this sequence.

prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.

prime 16-tuplets: A257308 out of A257369, A257370.

prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.

Programs

Perl

use bigint; use ntheory ":all"; say for sieve_prime_cluster(1, 10**17, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 50); # Dana Jacobsen, Oct 18 2015