Prime Numbers

Author : Dimitris Koukoulopoulos
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 48,6 Mb
Release : 2020-07-28
Category : Education
ISBN : 9781470462857

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The Distribution of Prime Numbers by Dimitris Koukoulopoulos Pdf

Prime numbers have fascinated mathematicians since the time of Euclid. This book presents some of our best tools to capture the properties of these fundamental objects, beginning with the most basic notions of asymptotic estimates and arriving at the forefront of mathematical research. Detailed proofs of the recent spectacular advances on small and large gaps between primes are made accessible for the first time in textbook form. Some other highlights include an introduction to probabilistic methods, a detailed study of sieves, and elements of the theory of pretentious multiplicative functions leading to a proof of Linnik's theorem. Throughout, the emphasis has been placed on explaining the main ideas rather than the most general results available. As a result, several methods are presented in terms of concrete examples that simplify technical details, and theorems are stated in a form that facilitates the understanding of their proof at the cost of sacrificing some generality. Each chapter concludes with numerous exercises of various levels of difficulty aimed to exemplify the material, as well as to expose the readers to more advanced topics and point them to further reading sources.

Author : David Wells
Publisher : Turner Publishing Company
Page : 260 pages
File Size : 54,8 Mb
Release : 2011-01-13
Category : Mathematics
ISBN : 9781118045718

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Prime Numbers by David Wells Pdf

A fascinating journey into the mind-bending world of prime numbers Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers? What did Albert Wilansky find so fascinating about his brother-in-law's phone number? Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions. In Prime Numbers: The Most Mysterious Figures in Math, you'll meet the world's most gifted mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd?o?s, and you'll discover a host of unique insights and inventive conjectures that have both enlarged our understanding and deepened the mystique of prime numbers. This comprehensive, A-to-Z guide covers everything you ever wanted to know--and much more that you never suspected--about prime numbers, including: * The unproven Riemann hypothesis and the power of the zeta function * The "Primes is in P" algorithm * The sieve of Eratosthenes of Cyrene * Fermat and Fibonacci numbers * The Great Internet Mersenne Prime Search * And much, much more

Author : Albert Edward Ingham
Publisher : Cambridge University Press
Page : 140 pages
File Size : 52,5 Mb
Release : 1990-09-28
Category : Mathematics
ISBN : 0521397898

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The Distribution of Prime Numbers by Albert Edward Ingham Pdf

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 : Gerald Tenenbaum,Michel Mendès France
Publisher : American Mathematical Soc.
Page : 137 pages
File Size : 41,9 Mb
Release : 2000
Category : Numbers, Prime
ISBN : 9780821816479

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The Prime Numbers and Their Distribution by Gerald Tenenbaum,Michel Mendès France Pdf

One notable new direction this century in the study of primes has been the influx of ideas from probability. The goal of this book is to provide insights into the prime numbers and to describe how a sequence so tautly determined can incorporate such a striking amount of randomness. The book opens with some classic topics of number theory. It ends with a discussion of some of the outstanding conjectures in number theory. In between are an excellent chapter on the stochastic properties of primes and a walk through an elementary proof of the Prime Number Theorem. This book is suitable for anyone who has had a little number theory and some advanced calculus involving estimates. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.

Author : Luogeng Hua
Publisher : American Mathematical Soc.
Page : 206 pages
File Size : 46,5 Mb
Release : 2009-12-04
Category : Mathematics
ISBN : 9780821849422

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Additive Theory of Prime Numbers by Luogeng Hua Pdf

Loo-Keng Hua was a master mathematician, best known for his work using analytic methods in number theory. In particular, Hua is remembered for his contributions to Waring's Problem and his estimates of trigonometric sums. Additive Theory of Prime Numbers is an exposition of the classic methods as well as Hua's own techniques, many of which have now also become classic. An essential starting point is Vinogradov's mean-value theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the Waring-Goldbach problem and gives asymptotic formulas for the number of solutions in Waring's Problem when the monomial $x^k$ is replaced by an arbitrary polynomial of degree $k$. The book is an excellent entry point for readers interested in additive number theory. It will also be of value to those interested in the development of the now classic methods of the subject.

Author : Denise Gaskins
Publisher : Tabletop Academy Press
Page : 288 pages
File Size : 42,5 Mb
Release : 2012-09-04
Category : Education
ISBN : 9781892083241

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Let's Play Math by Denise Gaskins Pdf

Author : Richard Crandall,Carl B. Pomerance
Publisher : Springer Science & Business Media
Page : 597 pages
File Size : 42,9 Mb
Release : 2006-04-07
Category : Mathematics
ISBN : 9780387289793

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Prime Numbers by Richard Crandall,Carl B. Pomerance Pdf

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 : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 558 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207597

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The New Book of Prime Number Records by Paulo Ribenboim Pdf

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.

Author : Barry Mazur,William Stein
Publisher : Cambridge University Press
Page : 155 pages
File Size : 42,8 Mb
Release : 2016-04-11
Category : Mathematics
ISBN : 9781107101920

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Prime Numbers and the Riemann Hypothesis by Barry Mazur,William Stein Pdf

This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.

Author : Paolo Giordano
Publisher : Penguin Canada
Page : 246 pages
File Size : 52,5 Mb
Release : 2010-03-23
Category : Fiction
ISBN : 9780143178293

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The Solitude of Prime Numbers by Paolo Giordano Pdf

A prime number is a lonely thing. It can be divided only by itself or by one; it never truly fits with another. Alice and Mattia are both “primes”—misfits who seem destined to be alone. Haunted by childhood tragedies that mark their lives, they find themselves unable to reach out to anyone else. When the two meet as teenagers, they recognize in each other a kindred, damaged spirit. As they grow into adulthood their destinies seem irrevocably intertwined. But when Mattia accepts a research position that takes him thousands of miles away, the two are forced to separate with many things left unsaid. A chance encounter will reunite them and force a lifetime of concealed emotion to the surface, but the question remains: Can two prime numbers ever find a way to be together? The Solitude of Prime Numbers is a stunning meditation on loneliness, love, and the weight of childhood experience.

Author : Thomas Lin
Publisher : MIT Press
Page : 331 pages
File Size : 50,8 Mb
Release : 2018-11-20
Category : Mathematics
ISBN : 9780262536356

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The Prime Number Conspiracy by Thomas Lin Pdf

The Pulitzer Prize–winning magazine’s stories of mathematical explorations show that inspiration strikes haphazardly, revealing surprising solutions and exciting discoveries—with a foreword by James Gleick These stories from Quanta Magazine map the routes of mathematical exploration, showing readers how cutting-edge research is done, while illuminating the productive tension between conjecture and proof, theory and intuition. The stories show that, as James Gleick puts it in the foreword, “inspiration strikes willy-nilly.” One researcher thinks of quantum chaotic systems at a bus stop; another suddenly realizes a path to proving a theorem of number theory while in a friend's backyard; a statistician has a “bathroom sink epiphany” and discovers the key to solving the Gaussian correlation inequality. Readers of The Prime Number Conspiracy, says Quanta editor-in-chief Thomas Lin, are headed on “breathtaking intellectual journeys to the bleeding edge of discovery strapped to the narrative rocket of humanity's never-ending pursuit of knowledge.” Winner of the 2022 Pulitzer Prize for Explanatory Reporting, Quanta is the only popular publication that offers in-depth coverage of the latest breakthroughs in understanding our mathematical universe. It communicates mathematics by taking it seriously, wrestling with difficult concepts and clearly explaining them in a way that speaks to our innate curiosity about our world and ourselves. Readers of this volume will learn that prime numbers have decided preferences about the final digits of the primes that immediately follow them (the “conspiracy” of the title); consider whether math is the universal language of nature (allowing for “a unified theory of randomness”); discover surprising solutions (including a pentagon tiling proof that solves a century-old math problem); ponder the limits of computation; measure infinity; and explore the eternal question “Is mathematics good for you?” Contributors Ariel Bleicher, Robbert Dijkgraaf, Kevin Hartnett, Erica Klarreich, Thomas Lin, John Pavlus, Siobhan Roberts, Natalie Wolchover Copublished with Quanta Magazine

Author : Vicky Neale
Publisher : Oxford University Press
Page : 208 pages
File Size : 49,5 Mb
Release : 2017-09-29
Category : Mathematics
ISBN : 9780191092435

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Closing the Gap by Vicky Neale Pdf

In 2013, a little known mathematician in his late 50s stunned the mathematical community with a breakthrough on an age-old problem about prime numbers. Since then, there has been further dramatic progress on the problem, thanks to the efforts of a large-scale online collaborative effort of a type that would have been unthinkable in mathematics a couple of decades ago, and the insight and creativity of a young mathematician at the start of his career. Prime numbers have intrigued, inspired and infuriated mathematicians for millennia. Every school student studies prime numbers and can appreciate their beauty, and yet mathematicians' difficulty with answering some seemingly simple questions about them reveals the depth and subtlety of prime numbers. Vicky Neale charts the recent progress towards proving the famous Twin Primes Conjecture, and the very different ways in which the breakthroughs have been made: a solo mathematician working in isolation and obscurity, and a large collaboration that is more public than any previous collaborative effort in mathematics and that reveals much about how mathematicians go about their work. Interleaved with this story are highlights from a significantly older tale, going back two thousand years and more, of mathematicians' efforts to comprehend the beauty and unlock the mysteries of the prime numbers.

Author : János Pintz,Michael Th. Rassias
Publisher : Springer
Page : 217 pages
File Size : 43,5 Mb
Release : 2018-07-04
Category : Mathematics
ISBN : 9783319927770

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Irregularities in the Distribution of Prime Numbers by János Pintz,Michael Th. Rassias Pdf

This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes. Written by an international group of experts, contributions present a self-contained yet unified exploration of a rapidly progressing area. Emphasis is given to the research inspired by Maier’s matrix method, which established a newfound understanding of the distribution of primes. Additionally, the book provides an historical overview of a large body of research in analytic number theory and approximation theory. The papers published within are intended as reference tools for graduate students and researchers in mathematics.

Author : H. Riesel
Publisher : Unknown
Page : 484 pages
File Size : 44,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475710909

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Prime Numbers and Computer Methods for Factorization by H. Riesel Pdf

Author : Thamer Naouech
Publisher : Independently Published
Page : 0 pages
File Size : 46,8 Mb
Release : 2020-10-20
Category : Electronic
ISBN : 9798839533677

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Prime Numbers, The Holy Grail Of Mathematics by Thamer Naouech Pdf

Prime numbers are undeniably one of the most beautiful and fascinating topics in mathematics. But what are prime numbers? Are they only numbers that are divisible by one 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. All of them attempted to solve the puzzling problem of primes. The achievements they realized and the secrets they revealed can only affirm how deep prime numbers are. 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 dark 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 Stanislaw 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".