# 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

**-2**

**0**answers

### Prime constellations, Chebotarev density theorem and Hardy-Littlewood $k$-tuple conjecture

**0**

**0**answers

### Prime constellation containing the primes in $[n-r_{0}(n),n+r_{0}(n)]$

**1**

**1**answer

### Symmetry in Hardy-Littlewood k-tuple conjecture

**1**

**0**answers

### $t$-balanced numbers

**5**

**0**answers

### On a conjecture about the arithmetic function that counts the number of twin primes

**2**

**0**answers

### Is this conjecture equivalent to Polignac's conjecture?

**1**

**1**answer

### Odd perfect numbers having as prime factors exclusively Mersenne primes and Fermat primes

**0**

**0**answers

### A conditional approach to twin prime conjecture

**0**

**0**answers

### Brocard's conjecture for Ramanujan primes

**1**

**0**answers

### Asymptotic behaviour of $\sum_{k=1}^{n}\frac{R_{k+1}+R_k}{R_{k+1}-R_k}$, where $R_k$ are the Ramanujan primes

**0**

**0**answers

### What about a second Hardy–Littlewood conjecture for Beatty primes?

**1**

**1**answer

### Are there infinitely many primes of the form $\frac{3a^2-a}{2}+b^4$?

**0**

**1**answer

### On the quantity of twin prime pairs of a given form

**0**

**1**answer

### Is this theorem on the abundance of prime patterns/k-tuples known?

**1**

**1**answer

### A question about a sum that involves gaps between twin primes, on assumption of the First Hardy–Littlewood conjecture

**2**

**1**answer

### On $\sum_{\substack{p\leq x\\p,p+2\text{ twin primes}}}\frac{(\log p)^m}{p}$, on assumption of the first Hardy–Littlewood conjecture

**0**

**0**answers

### What about an alternative formulation for different prime constellations in the spirit of Suzuki's theorem for twin primes?

**4**

**1**answer

### Arithmetic properties of a sum related to the first Hardy-Littlewood conjecture

**0**

**1**answer

### Sergei numbers : even integers n being a prime gap at least n times

**-3**

**1**answer

### Can this weakening of Polignac's conjecture be proven?

**1**

**0**answers

### Are the elements in the n-th row of the first matrix a permutation of the elements in the n-th row of the second matrix?

**4**

**0**answers

### Euclides' sieve

**3**

**0**answers

### Is the conjunction of Goldbach and NFPR conjecture actually equivalent to Hardy-Littlewood k-tuple conjecture?

**1**

**1**answer

### Admissible k-tuples and primorials

**4**

**1**answer

### Do prime gaps that are a power of “h” have the same density?

**0**

**2**answers

### On a coprime generalization of Cramer's conjecture

**0**

**1**answer

### What is the narrowest interval I=[a,b] such that there are infinitely prime gaps of size in I?

**4**

**0**answers

### Are prime gaps of even index essentially larger than those of odd index?

**1**

**1**answer

### Methods for searching for prime generating polynomials

**3**

**0**answers

### Does data suggest $| \pi_2 (n) - 2\Pi \int_2^n \frac{dx}{\ln(x)^2} | < \ln(n+2)^2 \sqrt (n+2) $?

**2**

**1**answer

### Counting function for prime pair with bounded gaps between them [duplicate]

**2**

**0**answers

### Does the proof of Conjectures B and D of Hardy and Littlewood have any implication on the generalized Riemann hypothesis they used?

**0**

**3**answers

### Has this formula for $G_{k}:=\lim\inf_{n\to\infty}p_{n+k}-p_{n}$ been conjectured?

**1**

**2**answers

### Primes as uncorrelated random variables [closed]

**2**

**1**answer