login
Initial primes in prime quadruplets (p, p+2, p+6, p+8) preceding the maximal gaps in A113404.
3

%I #16 Jan 15 2019 18:07:05

%S 5,11,191,821,2081,3461,5651,25301,34841,88811,122201,171161,301991,

%T 739391,1410971,1468631,2990831,3741161,5074871,5527001,8926451,

%U 17186591,21872441,47615831,66714671,76384661,87607361,122033201,132574061,204335771

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

%C 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.

%H Alexei Kourbatov, <a href="/A229907/b229907.txt">Table of n, a(n) for n = 1..71</a>

%H Tony Forbes, <a href="http://anthony.d.forbes.googlepages.com/ktuplets.htm">Prime k-tuplets</a>

%H Alexei Kourbatov, <a href="http://www.javascripter.net/math/primes/maximalgapsbetweenktuples.htm#4tuples">Maximal gaps between prime k-tuples</a>

%H Alexei Kourbatov, <a href="http://arxiv.org/abs/1309.4053">Tables of record gaps between prime constellations</a>, arXiv preprint arXiv:1309.4053 [math.NT], 2013.

%H Alexei Kourbatov and Marek Wolf, <a href="http://arxiv.org/abs/1901.03785">Predicting maximal gaps in sets of primes</a>, arXiv preprint arXiv:1901.03785 [math.NT], 2019.

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/k-TupleConjecture.html">k-Tuple Conjecture</a>

%e Record gaps between prime quadruplets are as follows (arXiv:1309.4053, Table 4):

%e Initial primes: Max gap

%e .....5......11........6

%e ....11.....101.......90

%e ...191.....821......630

%e ...821....1481......660

%e ..2081....3251.....1170

%e ..3461....5651.....2190

%e ..5651....9431.....3780

%e ...

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

%Y Cf. A007530, A113403, A113404.

%K nonn

%O 1,1

%A _Alexei Kourbatov_, Dec 19 2013