A257137 Numbers n such that n, n+4, n+6, n+10, n+16, n+18, n+24, n+28, n+30, n+34, n+40, n+46 and n+48 are all prime.

13, 4289907938811613, 5693002600430263, 21817283854511263, 48290946353555023, 51165618791484133, 53094081535451893, 70219878257874463, 98633358468021313, 99142644093930373, 104814760374339133, 166784569423739203, 167841416726358493, 184601252515266523, 263331429949004353, 272039012072134243, 339094624362619243, 363319822006646623, 363760043662280383, 437335541550793003, 455289126169953193

Offset: 1

Author

Tim Johannes Ohrtmann, Apr 16 2015

Keywords

• nonn

Comments

From Robert Israel, Aug 27 2015: (Start)

All terms after the first == 1483 (mod 2730).

n+4, n+16, n+28, n+46 are in A001359. (End)

Links

• Vladimir Vlesycit and Matt C. Anderson and Dana Jacobsen, Table of n, a(n) for n = 1..944 [first 21 terms from Vladimir Vlesycit, first 99 terms from Matt C. Anderson]
• Tony Forbes and Norman Luhn, Smallest Prime k-tuplets
• Norman Luhn, Table of n, a(n) for n = 1..6305

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, this sequence, A257138, A257139, A257140, A257141.

prime 14-tuplets: A257166 out of A257167, 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

PARI

is(n)=isp=isprime; isp(n) && isp(n+4) && isp(n+6) && isp(n+10) && isp(n+16) && isp(n+18) && isp(n+24) && isp(n+28) && isp(n+30) && isp(n+34) && isp(n+40) && isp(n+46) && isp(n+48) \\ Anders Hellström, Sep 05 2015

Perl

use ntheory ":all"; say for sieve_prime_cluster(1,10**16, 4,6,10,16,18,24,28,30,34,40,46,48); # Dana Jacobsen, Oct 07 2015