Related papers: Absolute Primes
This article is a collected information from some books and papers, and in most cases the original sentences is reserved about twin prime conjecture.
We introduce extremely symmetric primes and provide some elementary properties of these.
I give some claims on primorial prime numbers for interested readers in number theory.
A survey paper on some recent results on additive problems with prime powers.
We present a simple, closed formula which gives all the primes in order. It is a simple product of integer floor and ceiling functions.
This paper describes the construction of the first explicitly known widely digitally delicate prime.
In this paper, we give a complete description of the associated primes of each power of the edge ideal of an increasing weighted tree.
We survey the classical results on the prime number theorem
We present a variety of prime-generating constructions that are based on sums of primes. The constructions come in all shapes and sizes, varying in the number of dimensions and number of generated primes. Our best result is a construction…
We study a special set of constellations of primes generated by twin primes.
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…
In this note we generalise a method of Perott to give new proofs that there are infinitely many prime numbers.
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 -…
The set of prime numbers has been analyzed, based on their algebraic and arithmetical structure. Here by obtaining a sort of linear formula for the set of prime numbers, they are redefined and identified; under a systematic procedure it has…
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…
The author states an exact expression of the distribution of primes.
In this paper, we establish some theorems on the distribution of primes in higher-order progressions on average.
Comparative prime number theory is the study of the {\em{discrepancies}} of distributions when we compare the number of primes in different residue classes. This work presents a list of the problems being investigated in comparative prime…
The purpose of this article is to define and examine graded almost prime ideals over a non-commutative graded ring, and consider some cases where all graded right ideals of a non-commutative graded ring are graded almost prime.
This paper is devoted to the theory of prime numbers. In this paper we first introduce the notion of a matrix of prime numbers. Then, in order to investigate the density of prime numbers in separate rows of the matrix under consideration,…