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
Keywords
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.
Programs
-
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 *) -
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
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