Related papers: Absolute Primes

The present paper studies structure of the ring of integer-valued entire functions. We characterize certain classes of prime and maximal ideals and investigate some of their properties.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

For the edge ideal I of an arbitrary simple graph G we describe the monomials of the saturation of a power of I in terms of (vertex) weighted graphs associated with the monomials. This description allows us to characterize the embedded…

In the paper, the occurrence of zeros and ones in the binary expansion of the primes is studied. In particular the statement in the title is established. The proof is unconditional.

A hypothesis is put forward regarding the function $\pi_2(x)$ which describes the distribution of twin primes in the set of natural numbers. The function $\pi_2(x)$ is tested by evaluation and an empirical $\pi_2^{\ast}(x)$ is arrived at,…

We study pairs of consecutive odd numbers through a straightforward indexing. We focus in particular on twin primes and their distribution. With a counting argument, we calculate the limit of an alternating sum that is equal to 1 which…

We prove that every integer greater than two may be written as the sum of a prime and a square-free number.

We continue our recent work on averages for ternary additive problems with powers of prime numbers.

In this short paper we present an elementary proof of the infinitude of primes. Our proof is similar in spirit to Euler's proof that the reciprocals of primes diverges and only uses tools from elementary number theory and calculus. In…

We present a characterization of the finite groups in which all real classes have prime powers size.

Formula for the nth prime using elementary arithmetical functions based in a previous formula changing the characteristic function of prime numbers.

This paper describes some of the ideas used in the development of our work on small gaps between primes.

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

This is a survey article on prime number races. Chebyshev noticed in the first half of the nineteenth century that for any given value of x, there always seem to be more primes of the form 4n+3 less than x then there are of the form 4n+1.…

In this paper, we aim to introduce and study the notion of Endo-prime hyperideals.

In this paper, we give a complete description of the associated primes of every power of the edge ideal in terms of generalized ear decompositions of the graph. This result establishes a surprising relationship between two seemingly…

On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.

Let R be a multiplicative hyperring. In this paper, we define the concept of 1-absorbing prime hyperideals which is a generalization of the prime hyperideals. Several properties of the hyperideals are provided. Moreover, we introduce the…

Six conjectures on pairs of consecutive primes are listed in this paper, together with examples for each case.

This is a survey paper on the subject of strong uniqueness in approximation theory.