相关论文: Note on the Prime Number Theorem

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

Prime numbers have attracted the attention of mathematiciansand enthusiasts for millenniums due to their simple definition and remarkable properties. In this paper, we study primorial numbers (the product of the first prime numbers) to…

In this note we prove an inequality involving primes and the product of consecutive primes.

The main results extend to sums over primes in a short interval earlier estimates by the author for "long" Weyl sums over primes.

In this note I provide two extensions of a particular case of the classical Poncelet theorem.

This article provides a proof of the famous \textit{Prime Number Theorem} by establishing an analogous statement of the same in terms of the second \textit{Chebyshev Function} $\psi(x)$. We shall be extensively using complex analytic…

Most prime gaps results have been proven using tools from analytic or algebraic number theory in the last few centuries. In this paper, we would like to present some probabilistic way of proving many essential results. A major component of…

We present a simple, closed formula which gives all the primes in order. It is a simple product of integer floor and ceiling functions.

We continue investigations on the average number of representations of a large positive integer as a sum of given powers of prime numbers. The average is taken over a short interval, whose admissible length depends on whether or not we…

A survey paper on some recent results on additive problems with prime powers.

A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.

This work is meant to demonstrate new class of prime numbers -- cyclic prime numbers, that can be derived from any prime number at certain numeric systems. Cyclic prime numbers are also related to the cyclic numbers and full reptend prime…

In the present work the existence of some patterns of primes is shown which generalize the celebrated result of Green and Tao according to which there are arbitrarily long arithmetic progressions in the sequence of primes

We prove that several results in different areas of number theory such as the divergent series, summation of arithmetic functions, uniform distribution modulo one and summation over prime numbers which are currently considered to be…

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,…

I study the sequences of Euler and Springer numbers from the point of view of the classical moment problem.

We present some new ideas on important problems related to primes. The topics of our discussion are: simple formulae for primes, twin primes, Sophie Germain primes, prime tuples less than or equal to a predefined number, and their…

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.

By using the elementary symmetric polynomials and some results of number theory, we solve the well known problem of Lehmer on Euler's totient function. As application, we obtain a new characterization of prime numbers.

We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.