Related papers: A Dynamical Proof of the Prime Number Theorem

Let $p_n$ be $n$th prime, and let $(S_n)_{n=1}^\infty:=(S_n)$ be the sequence of the sums of the first $2n$ consecutive primes, that is, $S_n=\sum_{k=1}^{2n}p_k$ with $n=1,2,\ldots$. Heuristic arguments supported by the corresponding…

We give a new short proof of the most simple relation between consecutive power sums of the first m positive integers.

The theorem below gives another way of computing the distribution prime counting function without using recursion and the values of Prime numbers

In 1737 Leonard Euler gave what we often now think of as a new proof, based on infinite series, of Euclid's theorem that there are infinitely many prime numbers. Our short paper uses a simple modification of Euler's argument to obtain new…

The chronicle of prime numbers travel back thousands of years in human history. Not only the traits of prime numbers have surprised people, but also all those endeavors made for ages to find a pattern in the appearance of prime numbers has…

We found a regularity of the behavior of primes that allows to represent both prime and natural numbers as infinite matrices with a common formation rule of their rows. This regularity determines a new class of infinite cyclic groups that…

We showed that the prime gap for a prime number p is less than or equal to the prime count of the prime number.

We present an elementary proof for Ljunggren equation

We consider primitive divisors of terms of integer sequences defined by quadratic polynomials. Apart from some small counterexamples, when a term has a primitive divisor, that primitive divisor is unique. It seems likely that the number of…

In this note we give a detailed proof of a theorem of Aubin.

We provide a new proof for maximal monotonicity of the subdifferential of a convex function.

In this paper we present new, short and elementary proofs of the famous projection and section theorems that are used in Stochastic Calculus.

A dynamical analog of the prime ideals for simple non-commutative rings is introduced. We prove a factorization theorem for the dynamical ideals. The result is used to classify the surface knots and links in the smooth 4-dimensional…

Tao has shown that in any fixed base, a positive proportion of prime numbers cannot have any digit changed and remain prime. In other words, most primes are "digitally delicate". We strengthen this result in a manner suggested by Tao: A…

We introduce $p$-derivations and give a few basic ways in which they act like derivatives by numbers.

Two well known facts from elementary number theory are proven by using Bergman spaces.

A primorial prime is a prime number of the form $p_n\# \pm 1$ where $p_n\#$ denotes the product of all primes less than or equal to $p_{n}$, the $n$-th prime. We show that the probability along the lines of Mertens' Theorem that either…

We consider the immediate consequence of an arguable addition to the standard Deduction Theorems of first order theories.

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

In this work initial numbers and repunit numbers have been studied. All numbers have been considered in a decimal notation. The problem of simplicity of initial numbers has been studied. Interesting properties of numbers repunit are proved:…