A257167 Numbers n such that n, n+2, n+6, n+8, n+12, n+18, n+20, n+26, n+30, n+32, n+36, n+42, n+48 and n+50 are all prime.

11, 21817283854511261, 841262446570150721, 1006587882969594041, 2682372491413700201, 5009128141636113611, 7126352574372296381, 7993822923596334941, 12870536149631655611, 15762479629138737611, 22811391659969177381, 25593071201116914611, 25908823282383706781, 42408988436795325461, 44360646117391789301, 54533311498517797061, 54872625531142644341, 55603189618237916771, 60815831883653681951

Offset: 1

Author

Tim Johannes Ohrtmann, Apr 17 2015

Keywords

• nonn

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..185 [first 57 terms computed by Betsis, Säfholm, Forbes, Hadley, Vlesycit, and Waldvogel (1982-2009)]
• Tony Forbes and Norman Luhn, Smallest Prime k-tuplets
• Norman Luhn, Table of n, a(n) for n = 1..919

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 this sequence, A257168.

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 ntheory ":all"; say for sieve_prime_cluster(1, 10**17, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50); # Dana Jacobsen, Oct 18 2015

Extensions

a(32) corrected by Dana Jacobsen, Oct 18 2015