Related papers: Constellations of primes generated by twin primes

A modified Lagrange Polynomial is introduced for polynomial extrapolation, which can be used to estimate the equally spaced values of a polynomial function. As an example of its application, this article presents a prime-generating…

Wide gravitationally bound pairs of stars can be formed from adjacent prestellar cores that happen to move slowly enough relative to each other. These binaries are remnants of the primordial clustering. It is shown that the expected…

We present a new sieve that allows us to find the prime numbers by using only regular patterns and, more importantly, avoiding any duplication of elements between them.

Observations have revealed that most stars are born in clusters. These systems, containing from tens to thousands of stars and typically significant mass in gas in the youngest systems, evolve due to a combination of stellar and star-gas…

We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed field of prime characteristic.

We introduce the notion of saturated sets of primes of an algebraic number field and prove an analogue of Riemann's existence theorem for the decomposition groups of infinite stably saturated sets of primes.

We characterize all Gorenstein rings generated by strongly stable sets of monomials of degree two. We compute their Hilbert series in several cases, which also provides an answer to a question by Migliore and Nagel.

The overall frequency and other statistical properties of binary systems suggest that star formation is intrinsically a complex and chaotic process, and that most binaries and single stars actually originate from the decay of multiple…

Orthogonal sets of idempotents are used to design sets of unitary matrices, known as constellations, such that the modulus of the determinant of the difference of any two distinct elements is greater than $0$. It is shown that unitary…

We give some theoretical and computational results on "random" harmonic sums with prime numbers, and more generally, for integers with a fixed number of prime factors.

This paper describes the construction of the first explicitly known widely digitally delicate prime.

We investigate circular planar nearrings constructed from finite fields as well the complex number field using a multiplicative subgroup of order $k$, and characterize the overlaps of the basic graphs which arise in the associated…

We say that a prime number $p$ is an $\textit{Artin prime}$ for $g$ if $g$ mod $p$ generates the group $(\mathbb{Z}/p\mathbb{Z})^{\times}$. For appropriately chosen integers $d$ and $g$, we present a conjecture for the asymptotic number…

It is shown that any set of nonzero monomial prime ideals can be realized as the stable set of associated prime ideals of a monomial ideal. Moreover, an algorithm is given to compute the stable set of associated prime ideals of a monomial…

We show that the use of the main characteristics of the circle map leads naturally to establish a few statements on primes and pseudoprimes. In this way a Fermat's theorem on primes and some interesting properties of pseudoprimes are…

In the conference paper we construct analouge to Pascal's triangle that characterize primes with additional fascinating properties.

In this paper, the estimation formula of the number of primes in a given interval is obtained by using the prime distribution property. For any prime pairs $p>5$ and $ q>5 $, construct a disjoint infinite set sequence $A_1, A_2, \ldots,…

Preliminary results of the ongoing search for symbiotic binary stars in the Local Group of Galaxies are presented and discussed.

We present a model for the formation of high-mass close binary systems in the context of forming massive stars through gas accretion in the centres of stellar clusters. A low-mass wide binary evolves under mass accretion towards a high-mass…

This paper is about producing a new kind of the pairs which we call it MS-pairs. To produce these pairs, we use an algorithm for dividing a natural number $x$ by two for two arbitrary numbers and consider their related graphs. We present…