# Questions tagged [prime-constellations]

On certain subsets of prime numbers which are consecutive and close. Prime twins p and p+2, as well as p-2,p,p+4, are constellations. Also related are admissible sets in number theory, which are sets A of integers a_i such that there may be an integer t with many or all of t+a_i being prime. This has ties to prime gaps and additive number theory

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### The number of continuously increasing primes gaps in the interval $[2,n]$ is less than $\log n$

A prime gap is the difference between two successive prime numbers. The $n$-th prime gap, denoted gn or $g(p_n)$ is the difference between the $(n+1)$-st and the $n$-th prime numbers. Using my ...
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### Geometric prime distribution

Let integers $\ a>1\$ and $\ b\in\mathbb Z\$ be relatively prime (hence $\ b\ne 0).\$ The Dirichlet's prime distribution theorems apply to the arithmetic sequence $$(_aG_b(x) : x\in\mathbb Z)$$...
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### Is there a link between Elliott-Halberstam and weak Hardy-Littlewood-Goldbach conjectures?

Let $\theta$ be such that $EH(\theta)$ holds, where $EH$ stands for Elliott-Halberstam. Can one get an explicit lower bound $\delta_{\theta}$ for the quantity $\delta$ appearing in the weak Hardy-...
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### Prime constellations equivalent up to permutation

This question generalizes Symmetry in Hardy-Littlewood k-tuple conjecture. Say two prime constellations are equivalent up to permutation if they consist of the same multiset of prime gaps. One can ...
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### Measuring philoprimality/misoprimality

Given a natural integer $x$, let $$\alpha(x)=(\log x)^2\sum_{p\in\mathcal P\setminus\{x\}}\frac{1}{(x-p)^2}$$ (with $\mathcal P$ denoting the set of prime-numbers) measure its "philoprimality&...
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### On a conjecture about the arithmetic function that counts the number of twin primes

This is cross-posted from the question that I've asked with same title on Mathematics Stack Exchange two months ago, which has remained unanswered. Given a positive real number $x$ we will write ...
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### On quantities with no very small odd prime factors; a response to Wlodzimierz Holsztynski

In response to a comment posted under Powers of $2$ and the products of initial odd primes , I shall raise some questions about quantities near $O_n= P_{n+1}/2$, the product of the first $n$ odd ...
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