Related papers: Constellations of primes generated by twin primes
An odd prime labeling is a variation of a prime labeling in which the vertices of a graph of order~$n$ are labeled with the distinct odd integers $1$ to $2n-1$ so that the labels of adjacent vertices are relatively prime. This paper…
This paper considers a family of distributions constructed by a stochastic mixture of the order statistics of a sample of size two. Various properties of the proposed model are studied. We apply the model to extend the exponential and…
A well-known conjecture asserts that there are infinitely many primes $p$ for which $p - 1$ is a perfect square. We obtain upper and lower bounds of matching order on the number of pairs of distinct primes $p,q \le x$ for which $(p - 1)(q -…
We resolve the function field analogue of the conjecture concerning distribution of twin primes in arithmetic progression.
Large series of prime numbers can be superposed on a single quantum register and then analyzed in full parallelism. The construction of this Prime state is efficient, as it hinges on the use of a quantum version of any efficient primality…
We investigate the possibility of generating sizeable dipole radiations in relativistic theories of gravity. Optimal parameters to observe their effects through the orbital period decay of binary star systems are discussed. Constraints on…
This work proposes elementary proofs of several related primes counting problems, based on an elementary weighted sieve. The subsets of primes considered here are the followings: the subset of twin primes PT = {p and p + 2 are primes}, the…
We speculate on the distribution of primes in exponentially growing, linear recurrence sequences $(u_n)_{n\geq 0}$ in the integers. By tweaking a heuristic which is successfully used to predict the number of prime values of polynomials, we…
In this paper, spindle starshaped sets are introduced and investigated, which apart from normalization form an everywhere dense subfamily within the family of starshaped sets. We focus on proving spindle starshaped analogues of recent…
We study pairs of finitely generated modules over a principal ideal domain and their corresponding matrix representations. We introduce equivalence relations for such pairs and determine invariants and canonical forms.
In this paper, using the well known fact that the series of reciprocals of primes diverges, we obtain a general inequality for gaps of consecutive primes that holds for infinitely many primes. As it is shown the key ingredient for this…
We extend both Dobbertin's characterization of primely generated regular refinement monoids and Pierce's characterization of primitive monoids to general primely generated refinement monoids.
In this talk, I report results from galaxy merger simulations, which suggest the existence of a ring of star formation produced by close galaxy encounters. This is a generic feature of all galaxy interactions, provided that the disc spins…
The formation of massive stars is an outstanding problem in stellar evolution. However, it is expected that they are (predominantly) born in heirarchical environments within massive young clusters, which in turn are located within larger…
I give some claims on primorial prime numbers for interested readers in number theory.
We determine, in a polynomial ring over a field, the arithmetical rank of certain ideals generated by a set of monomials and one binomial.
The discovery of a population of young galaxies at an epoch when the universe was about one tenth of its current age has shed new light on the question of when and how galaxies formed. Within the context of popular models this is the…
In this brief note, we would like to point out that large-scale structures like galaxies and superclusters would arise quite naturally in the universe.
A new set of formulas for primes is presented. These formulas are more efficient and grow much slower than the two known formulas of Mills and Wright. 3 new formulas are explained.
We study the singularities of the projective dual variety.