Prime and Quasi-Prime Number Races
Author | : |
Publisher | : |
Total Pages | : |
Release | : 2009 |
Genre | : |
ISBN | : |
Download Prime and Quasi-Prime Number Races Book in PDF, Epub and Kindle
Download and Read Prime And Quasi Prime Number Races full books in PDF, ePUB, and Kindle. Read online free Prime And Quasi Prime Number Races ebook anywhere anytime directly on your device. We cannot guarantee that every ebooks is available!
Author | : |
Publisher | : |
Total Pages | : |
Release | : 2009 |
Genre | : |
ISBN | : |
Author | : Roger Plymen |
Publisher | : American Mathematical Soc. |
Total Pages | : 152 |
Release | : 2020-08-13 |
Genre | : Education |
ISBN | : 1470462575 |
Have you ever wondered about the explicit formulas in analytic number theory? This short book provides a streamlined and rigorous approach to the explicit formulas of Riemann and von Mangoldt. The race between the prime counting function and the logarithmic integral forms a motivating thread through the narrative, which emphasizes the interplay between the oscillatory terms in the Riemann formula and the Skewes number, the least number for which the prime number theorem undercounts the number of primes. Throughout the book, there are scholarly references to the pioneering work of Euler. The book includes a proof of the prime number theorem and outlines a proof of Littlewood's oscillation theorem before finishing with the current best numerical upper bounds on the Skewes number. This book is a unique text that provides all the mathematical background for understanding the Skewes number. Many exercises are included, with hints for solutions. This book is suitable for anyone with a first course in complex analysis. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.
Author | : Paulo Ribenboim |
Publisher | : Springer Science & Business Media |
Total Pages | : 492 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468499386 |
This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium series established to honour Professors A. J. Coleman and H. W. Ellis and to acknowledge their long-lasting interest in the quality of teaching undergraduate students. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book oj Records, reminded me very gently that the most "innumerate" people of the world are of a certain tribe in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes Morris, I'm from Brazil, but my book will contain numbers different from 'one.' " He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name), and consists of about 16 million digits of the number 11. "I assure you Morris, that in spite of the beauty of the apparent randomness of the decimal digits of 11, I'll be sure that my text will also include some words." Acknowledgment. The manuscript of this book was prepared on the word processor by Linda Nuttall. I wish to express my appreciation for the great care, speed, and competence of her work. Paulo Ribenboim CONTENTS Preface vii Guiding the Reader xiii Index of Notations xv Introduction Chapter 1. How Many Prime Numbers Are There? 3 I. Euclid's Proof 3 II.
Author | : Richard Crandall |
Publisher | : Springer Science & Business Media |
Total Pages | : 558 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468493167 |
Bridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Authors are well-known and highly-regarded in the field
Author | : Wladyslaw Narkiewicz |
Publisher | : Springer Science & Business Media |
Total Pages | : 457 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 3662131579 |
1. People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen ta, where we find a proof of their infinitude, now regarded as canonical. One feels that Euclid's argument has its place in The Book, often quoted by the late Paul ErdOs, where the ultimate forms of mathematical arguments are preserved. Proofs of most other results on prime number distribution seem to be still far away from their optimal form and the aim of this book is to present the development of methods with which such problems were attacked in the course of time. This is not a historical book since we refrain from giving biographical details of the people who have played a role in this development and we do not discuss the questions concerning why each particular person became in terested in primes, because, usually, exact answers to them are impossible to obtain. Our idea is to present the development of the theory of the distribu tion of prime numbers in the period starting in antiquity and concluding at the end of the first decade of the 20th century. We shall also present some later developments, mostly in short comments, although the reader will find certain exceptions to that rule. The period of the last 80 years was full of new ideas (we mention only the applications of trigonometrical sums or the advent of various sieve methods) and certainly demands a separate book.
Author | : G. J. O. Jameson |
Publisher | : Cambridge University Press |
Total Pages | : 266 |
Release | : 2003-04-17 |
Genre | : Mathematics |
ISBN | : 9780521891103 |
At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.
Author | : Thamer Naouech |
Publisher | : Thamer Naouech |
Total Pages | : 46 |
Release | : 2020-10-20 |
Genre | : Juvenile Nonfiction |
ISBN | : |
It is undeniable how prime numbers are one of the most beautiful and fascinating topics in mathematics. But what are prime numbers? Are they only numbers that are divisible by 1 and themselves, or do they have another interesting hidden face?Throughout history, the mystery of prime numbers has challenged the greatest minds in mathematics starting from Euclid of Alexandria to Fermat, Euler, Gauss, and Erdős,… who attempted to solve the puzzling problem of primes. The achievements they realized and the secrets they revealed can only assert how deep the concept of prime numbers is. Starting from how prime numbers exist in nature, and how they are of great use in modern cryptography on which our daily life completely depends, the author travels in the holy kingdom of primes diving into some conjectures involving those special numbers. From the Riemann Hypothesis and the well-known zeta function, he explains how a note in the margin turned to be Fermat’s Last Theorem, one of the most important problems in the history of mathematics. From Mersenne Primes, he gets to the twin primes, those shining little stars in the blue sky of primes. And from Euclid’s proof of the infinite number of primes he gets to a hidden pattern in the distribution of primes discovered by Stanisław Ulam and called the Ulam Spiral. After this little trip, you will know, dear reader, why prime numbers deserve to be called "the holy grail of mathematics".
Author | : Albert Edward Ingham |
Publisher | : Cambridge University Press |
Total Pages | : 140 |
Release | : 1990-09-28 |
Genre | : Mathematics |
ISBN | : 9780521397896 |
Originally published in 1934, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. Despite being long out of print, it remains unsurpassed as an introduction to the field.
Author | : Zwide Mbulawa |
Publisher | : Xlibris Corporation |
Total Pages | : 261 |
Release | : 2010-11-30 |
Genre | : Mathematics |
ISBN | : 1453598944 |
The Theory of Prime Number Classification This is an expository work of mathematical research into the prime numbers based on pattern methodology and classification techniques. As a comprehensive research into the classification systems for prime numbers, it address the following: „X Why prime numbers are regular yet random. „X What are the building blocks of prime numbers „X What is the framework for prime number generation This is done by developing the following classification systems: „X The Prime Root Classification. All prime numbers are constituted by roots, which are defined as the building blocks of the prime number. „X The Positional Classification. A two dimensional prime number space is defined that allows certain types of distribution analysis of primes to be made, deriving count functions and establishing the mean property of primes „X The Delta Classification of Primes. This classification creates prime families in terms of gaps. Prime gaps are found to have positive, negative and a steady gap acceleration. „X The Gap Theory Classification. All prime gaps and prime number behavior are based on Gap 2, Gap 4 and Gap 6. This then develops a classification system. Using the above classification systems, and defining a special function, a theory of prime number generation is then suggested, where this leads to the development of an algebraic sieve for finding prime numbers. The algebraic sieve contains all the relevant information about prime numbers, including how gaps widen, and prime number patterns. Consequently, it is then used to address the problem of finding a proof for the twin prime conjecture. As an expository work, the book also shares personal experiences and thoughts with regard to the research, and the development of expository mathematics. A program for prime number classification is available at www.zwideprimes.com
Author | : Paulo Ribenboim |
Publisher | : Springer Science & Business Media |
Total Pages | : 558 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461207592 |
This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium senes. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book of Records, reminded me very gently that the most "innumerate" people of the world are of a certain trible in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes, Morris, I'm from Brazil, but my book will contain numbers different from ·one.''' He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name) and consists of about 16 million decimal digits of the number Te. "I assure you, Morris, that in spite of the beauty of the appar ent randomness of the decimal digits of Te, I'll be sure that my text will include also some words." And then I proceeded putting together the magic combina tion of words and numbers, which became The Book of Prime Number Records. If you have seen it, only extreme curiosity could impel you to have this one in your hands. The New Book of Prime Number Records differs little from its predecessor in the general planning. But it contains new sections and updated records.