A035794 Start of a string of exactly 6 consecutive (but disjoint) pairs of twin primes.

325267931, 412984667, 2227604747, 2409360557, 4014288869, 4363839617, 6988064579, 8402566787, 9497780417, 10099096127, 12347083739, 12429980741, 13022601257, 14198015129, 14845029299, 15330685079, 16810761029, 17049454841, 18266059421, 18864084791

Offset

1,1

Links

Vasily Danilov, Table of n, a(n) for n = 1..10000, a(27)-a(41), a(112), a(227)-a(253) from Natalia Makarova, remaining terms from Vasily Danilov and Dmitry Petukhov.

Randall Rathbun, A study of n-twin_prime clusters among prime numbers, Posting to Number Theory List, Nov 19 1998.

Mathematica

fQ[n_] := Block[{k = 6}, And[NextPrime[n, -1] - NextPrime[n, -2] != 2, NextPrime[n, 2 k + 1] - NextPrime[n, 2 k] != 2, AllTrue[NextPrime[n, # + 1] - NextPrime[n, #] & /@ (Range[0, 2 k - 1, 2]), # == 2 &]]]; Select[Prime@ Range[10^9], fQ] (* Michael De Vlieger, May 09 2015, Version 10 *)

Prog

(PARI) isok(p) = {if (! isprime(p-2) && isprime(p+2), for (k=2, 6, my(q = nextprime(p+3)); if (! isprime(q+2), return (0)); p = q+2; ); q = nextprime(p+3); if (isprime(q+2), return (0)); return (1); ); return (0); } \\ Michel Marcus, Dec 06 2019

Crossrefs

Cf. A001359, A035789, A035790, A035791, A035792, A035793, A035794, A035795, A087641.

Sequence in context: A364265 A104923 A153753 * A260083 A344926 A344927

Adjacent sequences: A035791 A035792 A035793 * A035795 A035796 A035797

Keyword

nonn

Author

Randall L Rathbun

Extensions

a(11)-a(17) from Jud McCranie, Sep 16 2003

Offset corrected by Arkadiusz Wesolowski, May 06 2012

Wrong term 678771479 deleted and a(18)-a(26) from Sebastian Petzelberger, May 04 2015

Status

approved