A257141 Numbers n such that n, n+2, n+12, n+14, n+18, n+20, n+24, n+30, n+32, n+38, n+42, n+44 and n+48 are all prime.

10527733922579, 15991086371740199, 22443709342850669, 69759046409087909, 94415460183744419, 164873121596539229, 197053322268438509, 212971209388223159, 215768926871613989, 248170682800139819, 270109976153617319, 326374793491266239, 341896216415143109, 341987213500572359, 362035072661912369, 401062754451879239, 441180406661470349, 450928996714672349, 503035098004929209, 533306698691196149

Offset: 1

Author

Tim Johannes Ohrtmann, Apr 17 2015

Keywords

• nonn

Links

• Vladimir Vlesycit and Matt C. Anderson and Dana Jacobsen, Table of n, a(n) for n = 1..803 [first 20 terms from Vladimir Vlesycit, first 86 terms from Matt C. Anderson]
• Tony Forbes and Norman Luhn, Smallest Prime k-tuplets
• Norman Luhn, Table of n, a(n) for n = 1..5307 (Zip file)

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, this sequence.

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

isok(n)={isp=isprime;isp(n) &&isp(n+2)&&isp(n+12) &&isp(n+14) &&isp(n+18)&&isp(n+20)&&isp(n+24) &&isp(n+30) &&isp(n+32) &&isp(n+38) &&isp(n+42)&&isp(n+44)&&isp(n+48)} \\ Anders Hellström, Sep 05 2015

Perl

use ntheory ":all"; say for sieve_prime_cluster(1, 10**15, 2,12,14,18,20,24,30,32,38,42,44,48); # Dana Jacobsen, Oct 13 2015