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

Author

Bernardo Boncompagni, Oct 28 2005

Keywords

• nonn

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.

Examples

			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.
		

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.

Crossrefs

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