A113403 Primes p in prime quadruplets (p,p+2,p+6,p+8) at the end of maximal gaps in A113404.

11, 101, 821, 1481, 3251, 5651, 9431, 31721, 43781, 97841, 135461, 187631, 326141, 768191, 1440581, 1508621, 3047411, 3798071, 5146481, 5610461, 9020981, 17301041, 22030271, 47774891, 66885851, 76562021, 87797861, 122231111, 132842111, 204651611, 628641701, 1749878981

Offset

1,1

Comments

Prime quadruplets (p, p+2, p+6, p+8) are densest permissible constellations of four primes. Record (maximal) gaps between prime quadruplets are listed in A113404; see further comments there.

Links

Jud McCranie and Alexei Kourbatov, Table of n, a(n) for n = 1..71

Tony Forbes and Norman Luhn, Prime k-tuplets.

Alexei Kourbatov, Maximal gaps between prime k-tuples.

Alexei Kourbatov, Tables of record gaps between prime constellations, arXiv preprint arXiv:1309.4053, 2013.

Eric Weisstein's World of Mathematics, k-Tuple Conjecture.

Example

Record gaps between prime quadruplets are as follows (arXiv:1309.4053, Table 4):
Initial primes: Max gap
.....5......11........6
....11.....101.......90
...191.....821......630
...821....1481......660
..2081....3251.....1170
..3461....5651.....2190
..5651....9431.....3780
...
The left column is A229907. The middle column is A113403 (this sequence); the right column is A113404.

Crossrefs

Record gaps are given in A113404. Cf. A007530, A002386.

Sequence in context: A057532 A193699 A001603 * A045624 A125399 A163146

Adjacent sequences: A113400 A113401 A113402 * A113404 A113405 A113406

Keyword

nonn

Author

Bernardo Boncompagni, Oct 28 2005

Status

approved