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Prime Numbers
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 a...
The Prime Numbers and Their Distribution
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.
Prime Numbers, The Holy Grail Of Mathematics
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 c...
The World's Smallest Prime Number
This book contains the World's Smallest Prime Number. Nothing more, nothing less. Please do not buy it.
The Distribution of Prime Numbers
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 ...
The Distribution of Prime Numbers
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.
Closing the Gap
Since 2013, mathematicians from around the world have made dramatic progress on a problem in number theory that goes back centuries, the Twin Primes Conjecture, which asserts that there are infinitely many pairs of prime numbers that differ by 2 (for example, 17 and 19 is such a pair). This book describes two stories: that of the recent work on the Twin Primes Conjecture, and in parallel the related ideas around primes from the previous two thousand years ofmathematics.
The Book of Prime Number Records
This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquim series established to honor Professors A. J. Coleman and H. W. Ellis and to acknow ledge their long lasting interest in the quality of teaching under graduate students. In another colloquim lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guilllless Book oj Records, remainded 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 '...
The New Book of Prime Number Records
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 th...
Prime Numbers and the Riemann Hypothesis
This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
