Related papers: Gaps between primes
In this paper, we study the gaps between primes in Beatty sequences following the methods in the recent breakthrough of J. Maynard.
We studied two probabilistic models of the distribution of primes in the natural number [1].The paper considers the third probabilistic model of the distribution of primes in the natural number. The author proved that the results obtained…
A recent heuristic argument based on basic concepts in spectral analysis showed that the twin prime conjecture and a few other related primes counting problems are valid. A rigorous version of the spectral method, and a proof of the more…
It is a well-known fact that for any natural number $n$, there always exists a prime in $[n, 2n]$. Our aim in this note is to generalize this result to $[n, kn]$. A lower as well as an upper bound on the number of primes in $[n, kn]$ were…
This paper investigates the dependence between primes in tuples through the analysis of the Hardy-Littlewood constant. A detailed analysis of the behavior of the constant for the pattern $(0,d)$ is conducted, depending on the arithmetic…
In this note we prove an inequality involving primes and the product of consecutive primes.
The results of the previous version are impoved. This basically completes the study of consistency strength of various gaps between a strong limit singular cardinal of cofinality omega and its power under GCH type assumptions below.
Based on the primes less than $4 \times 10^{18}$, Oliveira e Silva et al. (2014) conjectured an asymptotic formula for the sum of the $k$th power of the gaps between consecutive primes less than a large number $x$. We show that the…
We give a counterexample to a recently conjectured variant of the Penrose inequality.
We survey research that studies the connection between the computational complexity of optimization problems on the one hand, and the duality gap between the primal and dual optimization problems on the other. To our knowledge, this is the…
This is a survey on Kawaguchi-Silverman conjecture.
We provide an alternative, simpler proof of the existence of thick triangulations for noncompact $\mathcal{C}^1$ manifolds. Moreover, this proof is simpler than the original one given in \cite{pe}, since it mainly uses tools of elementary…
We consider the representation of primes as a sum of a prime and twice a triangular number. We prove that a subset of the primes having density 1 is expressible in this form. We conjecture that every odd prime number is expressible as a sum…
We present new counterexamples, which provide stronger limitations to sums-differences statements than were previously known. The main idea is to consider non-uniform probability measures.
In the paper, there are new found methods to determine the range of every exceptional element in exceptional set, we can solve Twin primes problem and Goldbach Conjecture problem basically.
Under the prime-tuple hypothesis, the set of signed primes is a sumset.
We prove the topological analogue of the period-index conjecture in each dimension away from a small set of primes.
We consider the constraints on the fraction of dark matter in the universe in the form of primordial black holes taking into account the crucial role of accretion which may change both their mass and mass function. We show that accretion…
In this article we define a minor relation, which is stronger than the classical one, but too strong to become a well-quasi-order on the class of finite graphs. Nevertheless, with this terminology we are able to introduce a conjecture,…
In this paper, a simple explanation for the Goldbach Conjecture is given. We have shown that the probability of violating the conjecture not only for the prime numbers, but also for any subset of natural numbers whose distribution is…