Product Description

We have been curious about numbers--and prime numbers--since antiquity. 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. There are two ways in which the book is exceptional. First, some familiar topics are covered with refreshing insight and/or from new points of view. Second, interesting recent developments and ideas are presented that shed new light on the prime numbers and their distribution among the rest of the integers. The book begins with a chapter covering some classic topics, such as quadratic residues and the Sieve of Eratosthenes. Also discussed are other sieves, primes in cryptography, twin primes, and more. Two separate chapters address the Riemann zeta function and its connections to number theory. In the first chapter, the familiar link between $\zeta(s)$ and the distribution of primes is covered with remarkable efficiency and intuition. The second chapter presents a walk through an elementary proof of the Prime Number Theorem. To help the novice understand the "'why" of the proof, connections are made along the way with more familiar results such as Stirling's formula. A most distinctive chapter covers the stochastic properties of prime numbers. The authors present a wonderfully clever interpretation of primes in arithmetic progressions as a phenomenon in probability. They also describe Cramér's model, which provides a probabilistic intuition for formulating conjectures that have a habit of being true. In this context, they address interesting questions about equipartition modulo $1$ for sequences involving prime numbers. The final section of the chapter compares geometric visualizations of random sequences with the visualizations for similar sequences derived from the primes. The resulting pictures are striking and illuminating. The book concludes with a chapter on the outstanding big conjectures about prime numbers. 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. This book is the English translation from the French edition.

Product Details

• Amazon Sales Rank: #706972 in Books
• Published on: 2000-06-08
• Original language: English
• Binding: Paperback
• 115 pages

MAA Online
""A wonderful book ... marvelous." MAA Online"

Review
A wealth of information ... the exposition and the translation are excellent. (MAA Monthly )

A wonderful book ... marvelous. (MAA Online )

Customer Reviews

It was interessing, but lacked a bit of life in it.
I read this book about a month a go for my a-level background reading in advanced mathamatics a i thought that Gerald Teneembaum seems to have the idea that this book is for "people" who are higher than mortals and that the way the book is set out it makes it look complicated so that people will think that the book is good, the truth is that the book is good, interesting and cramed with amazing facts but the layout of the book takes away the quality, it is as if he didn't want people to understand and this was rather dissapointing. I advise that you buy this book if you are going to use for work, but not for background reading