Talk:Prime k-tuple

First Hardy-Littlewood Conjecture

There should be some statement of the First Hardy-Littlewood conjecture, which involves the density of primes fitting a given prime constellation. One consequence is on http://en.wikipedia.org/wiki/First_Hardy%E2%80%93Littlewood_conjecture#First_Hardy.E2.80.93Littlewood_conjecture but the full statement isn't given there. —Preceding unsigned comment added by 66.30.116.104 (talk) 17:57, 23 January 2010 (UTC)[reply]

It is mentioned in the article, in the last sentence of the Prime constellations section, and includes a wikilink to the subsection in Twin prime that covers it in more detail. I'm not sure if there's a need to repeat the material here, but if you'd like to rework the section to give it more prominence you're welcome to do so. --mwalimu59 (talk) 21:36, 23 January 2010 (UTC)[reply]

Ordered?

"In number theory, a prime k-tuple is an ordered set of values (i.e. a vector)" Why ordered? This is claiming that (0, 2, 6), (0, 6, 2) and (2, 0, 6) are distinct prime k-tuples. Moreover, a vector can have repeated elements, and so (0, 2, 6, 2) would be considered another prime k-tuple distinct from those I've already listed. Yet all the specific prime k-tuples mentioned in the article have the elements in ascending order and not repeated; moreover, I can't see any practial use for considering them distinct. It seems to me that, in reality, it is just a set.

Moreover, what does "smallest" mean? Fewest elements? Smallest sum of values? Smallest maximum value? — Smjg (talk) 23:31, 2 June 2012 (UTC)[reply]

You have to distinguish the k-tuples of primes from the k-tuples of differences, which are usually given as (p1-p1, p2-p1, p3-p1). But actually the patterns should be thought of (k-1)-tuples of first differences (or gaps) (p2-p1, p3-p2, ...). Obviously, here the order matters and the gaps will usually not be in increasing order. Anyway, a given k-tuples of primes occurs only once, it's the pattern of gaps that repeats. — MFH:Talk 13:09, 26 October 2018 (UTC)[reply]

A conjecture for prime k-tuple

If n, k are integers and n ≥ 2, k ≥ 1, then ther exists a prime k-tuple between n and (k+1)n, and the difference of the largest prime and the smallest prime in this tuple is at most k(k−1). (the primes in this tuple cannot include n or (k+1)n)

For example, for all integer n ≥ 2:

There is a prime between n and 2n.
There is twin primes between n and 3n.
There is a prime 3-tuple of one of the three forms: {p, p+2, p+4} (only for n = 2), {p, p+2, p+6}, and {p, p+4, p+6} between n and 4n.

— Preceding unsigned comment added by 49.217.146.70 (talk)

If you are making a suggestion for the article then Wikipedia:Verifiability says content must be based on published reliable sources. If you are not making a suggestion then note Wikipedia:Talk page guidelines#How to use article talk pages says talk pages are for discussing the article, not for general conversation about the article's subject. PrimeHunter (talk) 22:21, 13 May 2017 (UTC)[reply]

Tuple vs. tuplet

Apparently OEIS uses "tuplet" instead of "tuple", and MathWorld offers [a] prime constellation, also called a prime k-tuple, prime k-tuplet, or prime cluster on their "Prime Constellation" page. Wiktionary has tuple and tuplet, claiming that the latter is about music. IOW, how about adding prime tuplet as alias in the lede?

Unrelated and JFTR, I've upgraded class="stub" to class="start" on this talk page, because the page is no stub, but actually I think it should be class="B" or class="C". –178.24.246.213 (talk) 15:15, 13 November 2017 (UTC)[reply]

Conjecture about ratio of gaps

It seems quite obvious that the ratio of subsequent gaps g(n)/g(n+1) can be equal to any positive rational number a/b > 0. Also, if (n+1) is replaced by (n+j) for some larger integer j > 0. Is this a known "conjecture" ? Polignac's conjecture is about existence of gaps, but this here is related to "patterns" since we consider subsequent gaps. I think the pattern of gaps (6a, 6b) is admissible (i.e., will occur) for any a,b > 0 (and similarly with some other gaps in between, for the case j > 1), but it is not a constellation in the sense of being minimal. Can anyone give a reference related to that? — MFH:Talk 13:23, 26 October 2018 (UTC)[reply]