This site is supported by donations to The OEIS Foundation.



Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 4500 articles have referenced us, often saying "we would not have discovered this result without the OEIS".

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A201598 Record (maximal) gaps between prime triplets (p, p+2, p+6). 11
6, 24, 60, 84, 114, 180, 210, 264, 390, 564, 630, 1050, 1200, 1530, 2016, 2844, 3426, 3756, 3864, 3936, 4074, 4110, 6090, 8250, 9240, 9270, 10344, 10506, 10734, 10920, 12930, 15204, 20190, 20286, 21216, 25746, 34920, 38820, 39390, 41754, 43020, 44310, 52500, 71346 (list; graph; refs; listen; history; text; internal format)



Prime triplets (p, p+2, p+6) are one of the two types of densest permissible constellations of 3 primes (A022004 and A022005). By the Hardy-Littlewood k-tuple conjecture, average gaps between prime k-tuples are O(log^k(p)), with k=3 for triplets. If a gap is larger than any preceding gap, we call it a maximal gap, or a record gap. Maximal gaps may be significantly larger than average gaps; this sequence suggests that maximal gaps between triplets are O(log^4(p)).

A201599 lists initial primes p in triplets (p, p+2, p+6) preceding the maximal gaps. A233434 lists the corresponding primes p at the end of the maximal gaps.


Hardy, G. H. and Littlewood, J. E. "Some Problems of 'Partitio Numerorum.' III. On the Expression of a Number as a Sum of Primes." Acta Math. 44, 1-70, 1923.


Table of n, a(n) for n = 1..72

T. Forbes, Prime k-tuplets

Alexei Kourbatov, Maximal gaps between prime k-tuples

A. Kourbatov, Maximal gaps between prime k-tuples: a statistical approach, arXiv preprint arXiv:1301.2242, 2013. - From N. J. A. Sloane, Feb 09 2013

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

Alexei Kourbatov, The distribution of maximal prime gaps in Cramer's probabilistic model of primes, arXiv preprint arXiv:1401.6959, 2014

Eric W. Weisstein, k-Tuple Conjecture


Gaps between prime triplets (p, p+2, p+6) are smaller than 0.35*(log p)^4, where p is the prime at the end of the gap. There is no rigorous proof of this formula. The O(log^4(p)) growth rate is suggested by numerical data and heuristics based on probability considerations.


The gap of 6 between triplets starting at p=5 and p=11 is the very first gap, so a(1)=6. The gap of 6 between triplets starting at p=11 and p=17 is not a record, so it does not contribute to the sequence. The gap of 24 between triplets starting at p=17 and p=41 is a maximal gap - larger than any preceding gap; therefore a(2)=24.


Cf. A022004 (prime triplets p, p+2, p+6), A113274, A113404, A200503, A201596, A201062, A201073, A201051, A201251, A202281, A202361, A201599, A233434.

Sequence in context: A002653 A212904 A264790 * A211615 A195647 A086768

Adjacent sequences:  A201595 A201596 A201597 * A201599 A201600 A201601




Alexei Kourbatov, Dec 03 2011



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 30 00:53 EST 2015. Contains 264663 sequences.