Related papers: Finding a Widely Digitally Delicate Prime
In this paper, we investigate primeness of groupoid graded rings. We provide a set of necessary and sufficient conditions for primeness of a nearly-epsilon strongly groupoid graded ring. Furthermore, we apply our main result to get a…
We proved that there are infinitely many pairs of twin prime.
The twin primes conjecture is a very old problem. Tacitly it is supposed that the primes it deals with are finite. In the present paper we consider three problems that are not related to finite primes but deal with infinite integers. The…
We define S(um)anD(ifference) numbers as ordered pairs $(m,\, m+\Delta)$ such that the digital-sum $DS(m(m+\Delta))=\Delta.$ We consider both the decimal and the binary case. If both $m$ and $m+\Delta$ are prime numbers, we refer to SanD…
This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…
This primer is intended as an introduction to differential forms, a central object in modern mathematical physics, for scientists and engineers.
Two-dimensional lead halide perovskites are promising materials for optoelectronics due to the tunability of their properties with the number of lead halide layers and the choice of an organic spacer. Physical understanding for the rational…
The Painleve and weak Painleve conjectures have been used widely to identify new integrable nonlinear dynamical systems. The calculation of the integrals relies though on methods quite independent from Painlev\'e analysis. This paper…
It is shown that in the case of multicomponent integrable systems connected with algebras $A_n$, the discrete transformation $T$ possesses the fine structure and can be represented in the form $T=\prod T_i^{l_i}$, where $T_i$ are n…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
We shall realize certain affine geometric crystal of type $G^{(1)}_2$ explicitly in the fundamental representation $W(\varpi_1)$. Its explicit form is rather complicated but still keeps a positive structure.
Differentiable real function reproducing primes up to a given number and having a differentiable inverse function is constructed. This inverse function is compared with the Riemann-Von Mangoldt exact expression for the number of primes not…
We give an upper bound for the Matveev complexity of the whole class of closed connected orientable prime graph manifolds that is sharp for all 14502 graph manifolds of the Recognizer catalogue (available at…
Although the prime numbers are deterministic, they can be viewed, by some measures, as pseudo-random numbers. In this article, we numerically study the pair statistics of the primes using statistical-mechanical methods, especially the…
Statistical distribution of the primes in an arithmetic progression is considered. The estimation of prime numbers is given and combinatorial methods are used to calculate the twin primes on the available interval. The distribution and…
We give necessary conditions satisfied by the set of odd prime divisors of binary perfect polynomials. This allows us to get a new characterization of all the known perfect binary polynomials.
We generalize the differential dimension polynomial from prime differential ideals to characterizable differential ideals. Its computation is algorithmic, its degree and leading coefficient remain differential birational invariants, and it…
Define $\psi_m$ to be the smallest strong pseudoprime to the first $m$ prime bases. The exact value of $\psi_m$ is known for $1\le m \le 8$. Z. Zhang have found a 19-decimal-digit number $Q_{11}=3825\,12305\,65464\,13051$ which is a strong…
In this paper, we introduce $\phi$-$\delta$-primary elements in a compactly generated multiplicative lattice $L$ and obtain its characterizations. We prove many of its properties and investigate the relations between these structures. By a…