Related papers: The distribution of prime numbers
The pentagonal number theorem is extended to the sequence of the number of integer partitions with all parts equal. The new pentagonal number theorem implies that the distribution of the primes is just a specific detail of the application…
This set of Montreal lectures is an elementary and sketchy introduction to the general field of random matrices. The first half is devoted to combinatorial models, whereas the second half deals with random matrix questions(GUE, etc...).
This paper is devoted to the study of equidistributional properties of \textit{totient points} in $\mathbb{N}^r$, that is, of coprime $r$-tuples of integers, with particular emphasis on some relevant sets of totient points fulfilling extra…
We studied two probabilistic models of the distribution of primes in the natural number [1].The paper considers the third probabilistic model of the distribution of primes in the natural number. The author proved that the results obtained…
I give some claims on primorial prime numbers for interested readers in number theory.
The prime number problem falls within the realm of number theory, specifically elementary number theory. Current research approaches have unnecessarily complicated this matter. In contrast to more advanced mathematical tools, the methods of…
Definition of the number of prime numbers in the given interval
We study, from the viewpoint of metrical number theory and (infinite) ergodic theory, the probabilistic laws governing the occurrence of prime numbers as digits in continued fraction expansions of real numbers.
This is an exposition of recent developments in the theory of bounded differences between primes. Readers are expected to be beginners of analytic number theory. The present text is a substantially improved and augmented version of the one…
We investigate the distribution of the digits of quotients of randomly chosen positive integers taken from the interval $[1,T]$, improving the previously known error term for the counting function as $T\to+\infty$. We also resolve some…
This work consists of a heuristic study on the distribution of prime numbers in short intervals. We have modelled the occurrence of prime numbers such intervals as a counting experiment. As a result, we have provided an experimental…
The distribution of prime numbers is here considered. We show a formula for $li^{-1}$ and we study the $\pi(x)$ function and Riemann's hypothesis.
For $a \neq 1$ and $p$ prime, we define numbers of the form $pa^2$ to be Square-Prime (SP) Numbers. For example, 75 = 3 $\cdot$ 25; 108 = 3 $\cdot$ 36; 45 = 5 $\cdot$ 9. These numbers are listed in the OEIS as A228056. We study the…
This is an expository article to accompany my two lectures at the CDM conference. I have used this an excuse to make public two sets of notes I had lying around, and also to put together a short reader's guide to some recent joint work with…
In this work I look at the distribution of primes by calculation of an infinite number of intersections. For this I use the set of all numbers which are not elements of a certain times table in each case. I am able to show that it exists a…
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…
Prime numbers or primes are man's eternal treasures that have been cherished for several millennia, until today. As their academic ancestors in ancient Mesopotamia, many mathematicians are still trying hard to see primes better. I shall…
In this paper, we establish some theorems on the distribution of primes in higher-order progressions on average.
Simple divisibility rules are given for the 1st 1000 prime numbers.
We define and study a transform whose iterates bring to the fore interesting relations between Pisot numbers and primes. Although the relations we describe are general, they take a particular form in the Pisot limit points. We give three…