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

1,1

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

Prog

(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

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.

Sequence in context: A334634 A048847 A093671 * A134070 A257308 A257369

Adjacent sequences: A257134 A257135 A257136 * A257138 A257139 A257140

Keyword

nonn

Author

Tim Johannes Ohrtmann, Apr 16 2015

Status

approved