Related papers: Constellations of primes generated by twin primes
This paper investigates prime and co-prime integer matrices and their properties. It characterizes all pairwise co-prime integer matrices that are also prime integer matrices. This provides a simple way to construct families of pairwise…
Two minimal generating sets of the first syzygies of a monomial ideal are produced, given the minimal generating set of the ideal.
We proved that there are infinitely many cousin primes.
In this note, we propose simple summations for primes, which involve two finite nested sums and Bernoulli numbers. The summations can also be expressed in terms of Bernoulli polynomials.
A discrete duality is a relationship between classes of algebras and classes of relational systems (frames) resulting in two representation theorems building on the early work of J\'onsson and Tarski, Kripke, and van Benthem. In this…
We study odd numbers through a straightforward indexing. We focus in particular on odd prime and composite numbers and their distribution. With a counting argument, we calculate the limit of two sums and compare their convergence rate.
Let $\mathcal{A}'$ be the set of integers missing any three fixed digits from their decimal expansion. We produce primes in a thin sequence by proving an asymptotic formula for counting primes of the form $p = m^2 + \ell^2$, with $\ell \in…
In this paper, we establish some theorems on the distribution of primes in higher-order progressions on average.
Prime numbers are fascinating by the way they appear in the set of natural numbers. Despite several results enlighting us about their repartition, the set of prime numbers is often informally qualified as misterious. In the present paper,…
We review recent work that investigates the formation of stellar clusters, ranging in scale from globular clusters through open clusters to the small scale aggregates of stars observed in T associations. In all cases, recent advances in…
A recursive random number generator using prime reciprocals is described.
We study additively graceful labelings of signed graphs on stars and double stars. While the case of signed stars is straightforward, the problem becomes significantly more intricate for signed double stars. We obtain a characterization of…
We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.
We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.
For the sequence defined by a(n) = a(n-1) + gcd(n, a(n-1)) with a(1) = 7 we prove that a(n) - a(n-1) takes on only 1s and primes, making this recurrence a rare "naturally occurring" generator of primes. Toward a generalization of this…
The formation of massive stellar clusters in turbulent molecular clouds is investigated. We include artificial star formation and energy feedback of newly born stars. The obtained systems are not likely to survive. Case studies to determine…
It has been conjectured that a complete set of mutually unbiased bases in a space of dimension d exists if and only if there is an affine plane of order d. We introduce affine constellations and compare their existence properties with those…
We construct a rigid, rank 1, prime transformation that is not quasi-simple and whose self-joinings form a Paulsen simplex. This seems to be the first example of a prime system whose self-joinings form a Paulsen simplex.
In this document we consider the prime and maximal spectra of an MV-algebra with certain natural operations. Several new MV-algebras are constructed in this fashion.
In this paper we prove some new series for $1/\pi$ as well as related congruences. We also raise several new kinds of series for $1/\pi$ and present some related conjectural congruences involving representations of primes by binary…