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

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

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

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

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### 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

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

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### What about series involving strong primes?

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

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

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

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### 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?

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### Euclides' sieve

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

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

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### Admissible k-tuples and primorials

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

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

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### Methods for searching for prime generating polynomials

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

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

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

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

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

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### Primes as uncorrelated random variables [closed]

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