Related papers: Extremely symmetric primes

We introduce a sieve for counting twin primes up to a given range. Our method depends on a parameter ${\lambda}_x$ and the estimation of the number of twin primes obtained as a result, is called a fundamental structure of the distribution…

In this note, we approximate the average of prime powers in the decomposition of $n!$ into prime numbers.

We construct families of prime ideals in polynomial rings for which the number of associated primes of the second power (or higher powers) is exponential in the number of variables in the ring. We give a lower bound on the Ananyan-Hochster…

The present article includes the enumeration of $n$-polygons with a certain symmetry property: For an even number $n$ of vertices, we count the $n$-polygons with $\frac{n}{2}$ symmetry axes. In addition, if $n$ is a power of 2, we show the…

For earlier considered our sequence A166944 in [4] we prove three statements of its connection with twin primes. We also give a sufficient condition for the infinity of twin primes and pose several new conjectures; among them we propose a…

In this paper we find all complex symmetric weighted composition operators with special conjugations. Then we give spectral properties of these complex symmetric weighted composition operators.

We provide an elementary proof of an asymptotic formula for prime counting functions. As a minor application we give a new reduction of the proof of Chebotar\"ev's density theorem to the cyclic case.

We prove some isomorphisms between exceptional W-algebras associated with exceptional simple Lie algebras.

We present a class of one-to-one matching models with perfectly transferable utility. We discuss identification and inference in these separable models, and we show how their comparative statics are readily analyzed.

We give explicit numerical estimates for the generalized Chebyshev functions. Explicit results of this kind are useful for estimating of computational complexity of algorithms which generates special primes. Such primes are needed to…

In this paper, we show that under certain conditions on the coefficients and initial values, solutions of two different Bernoulli initial-value problems are symmetric to each other either with respect to the t-axis, or the y-axis, or the…

Several new identities for elliptic hypergeometric series are proved. Remarkably, some of these are elliptic analogues of identities for basic hypergeometric series that are balanced but not very-well-poised.

We present a versatile construction allowing one to obtain pairs of integer sets with infinite symmetric difference, infinite intersection, and identical representation functions.

We introduce three simple polynomial maps with integer coefficients that have interesting dynamical properties modulo primes.

A generalization of highly symmetric frames is presented by considering also projective stabilizers of frame vectors. This allows construction of highly symmetric line systems and study of highly symmetric frames in a more unified manner.…

In this paper, we define and study quasi S-primary hyperideals, weakly quasi S-hyperideals and strongly S-primary hyperideals.

We derived the sum identities for generalized harmonic and corresponding oscillatory numbers for which a sieve procedure can be applied. The obtained results enable us to understand better the properties of these numbers and their…

A linear combination $aT_r(m)+bT_s(n)$ of an \mbox{$r$-gonal} number $T_r(m)$ and an $s$-gonal number $T_s(n)$ with mutually coprime positive integer coefficients $a$ and $b$ produces infinitely many primes as $m$ and~$n$ varies over the…

This is an elementary introduction to basic tools of supersymmetry: the spacetime symmetries, gauge theory and its application in gravity, spinors and superalgebras. Special attention is devoted to conformal and anti-de Sitter algebras.

We introduce the notion of almost finite dimensionality of algebras and study its connection with the classical finiteness conditions.