In number theory, a prime k-tuple is a finite collection of values representing a repeatable pattern of differences between prime numbers. For a k-tuple (a, b, …), the positions where the k-tuple …

4 天之前 · The k-tuple conjecture states that the asymptotic number of prime constellations can be computed explicitly. In particular, unless there is a trivial divisibility condition that stops p, …

In this chapter, we review the work of Gallagher in the direction of the Hardy–Littlewood \(k\)-tuples conjecture, a vast (and quantitative) generalization of the twin primes conjecture.

2020年8月11日 · 这在生物学上很有用，寻找到高度相似的子序列，可能就是同源序列部分。 也被称为 k-tuple 方法，是一种启发式算法 (heuristic)，不追求最优比对但是比动态规划效率高很 …

1 The Hardy-Littlewood k-tuples conjecture Let H denote a k-tuple of distinct integers. What does one expect about the distribution of the integers n such that n+h is prime for each h 2 H? Here …

2020年8月25日 · We give sufficient conditions for the existence of increasing sequences of natural numbers aj and nk such that nk +haj is a sum of two squares for every k ≥ 1 and 1 ≤ j ≤ …

A prime k-tuplet is a sequence of k consecutive prime numbers such that in some sense the difference between the first and the last is as small as possible. The idea is to generalise the …

In mathematics, a k-tuple is an ordered set of k values (a vector of degree k): ( a 1 , a 2 , ..., a k ). When working in the context of prime numbers a k -tuple usually refers to a k -tuple of distinct …

2012年5月21日 · Weighted sieves have shown for infinitely many integers $n$ that $\Omega(\Pi(n))\le r_k$ holds for some integer $r_k$ which is asymptotic to $k\log{k}$. We …

A prime constellation, also called a prime k-tuple, prime k-tuplet, or prime cluster, is a sequence of k consecutive numbers such that the difference between the first and last is, in some sense, …