A229907 Initial primes in prime quadruplets (p, p+2, p+6, p+8) preceding the maximal gaps in A113404.

5, 11, 191, 821, 2081, 3461, 5651, 25301, 34841, 88811, 122201, 171161, 301991, 739391, 1410971, 1468631, 2990831, 3741161, 5074871, 5527001, 8926451, 17186591, 21872441, 47615831, 66714671, 76384661, 87607361, 122033201, 132574061, 204335771

Offset: 1

Author

Alexei Kourbatov, Dec 19 2013

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 this sequence (A229907). The middle column is A113403; the right column is A113404.
		

Links

• Alexei Kourbatov, Table of n, a(n) for n = 1..71
• Tony Forbes, 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 [math.NT], 2013.
• Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.
• Eric W. Weisstein, k-Tuple Conjecture

Crossrefs

Cf. A007530, A113403, A113404.