A deep understanding of prime numbers is one of the great challenges in mathematics. In this new edition, fundamental theorems, challenging open problems, and the most recent computational records are presented in a language without secrets. The impressive wealth of material and references will make this book a favorite companion and a source of inspiration to all readers. Paulo Ribenboim is Professor Emeritus at Queen's University in Canada, Fellow of the Royal Society of Canada, and recipient of the George Polya Award of the Mathematical Association of America. He is the author of 13 books and more than 150 research articles. From the reviews of the First Edition: Number Theory and mathematics as a whole will benefit from having such an accessible book exposing advanced material. There is no question that this book will succeed in exciting many new people to the beauty and fascination of prime numbers, and will probably bring more young people to research in these areas. (Andrew Granville, Zentralblatt)
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From the reviews of the second edition:
The Little Book of Big Primes
"Everyone has at one time or another taken an interest, however fleeting, in prime numbers . . . Ribenboim, however, is clearly a ‘prime nut,’ and this excellent, good-humored book is written for other (actually or potentially) incurable aficionados . . . it is a masterly presentation . . . This genially reader-friendly tour de force, by a scientist whit an encyclopedic and up-to-the-minute knowledge of the subject, is a wholly admirable addition to anyone’s bookshelf."?AMERICAN SCIENTIST
"The book presents a wealth of material and references on fundamental theorems, challenging open problems, and the most recent computational records in a language without secrets." (Zentralblatt für Didaktik und Mathematik, November, 2004)
"This book is the substantially expanded and updated second edition of the 1991 ‘Little book of big primes’. … The author’s thorough knowledge of and passion for primes comes through clearly. Most of the book is accessible even to interested amateurs or undergraduate students … . At the same time, a specialist can also find it useful to have so many results, open problems and references collected together." (Gábor Megyesi, Acta Scientiarum Mathematicarum, Vol. 72, 2006)
"One could say that Paul Ribenboim created a new genre of mathematical writing with the publication of ‘The Book of Prime Number Records.’. … This together with the author’s charming style, made it a success. The book under review is the abridged version of its successor ‘The New Book of Prime Number Records.’ … The reviewer believes that this book really has the ‘fatal attraction’ its author wishes it to exert." (Ch. Baxa, Monatshefte für Mathematik, Vol. 148 (1), 2006)
"This is a book of well documented records. … But this is a book of much more than records, providing as good an introduction as any to the theory of primes … . The first edition of the book appeared in 1991 … . It is here expanded and updated … . Throughout the book history, theory, specific cases and other results are woven into a compact but comprehensive presentation. A most useful resource for both teaching and research into the prime numbers." (Alan Sutcliffe, The Mathematical Gazette, Vol. 89 (516), 2005)
“The style of the book seems to stay with us: lucid, witting and very absorbing to both your time as well as your computer’s. Theories are introduced and explained well … . this is also fun reading for non-programming mathematicians … .” (Pieter Audenaert, Bulletin of the Belgian Mathematical Society, 2009)Contenuti:
How Many Prime Numbers Are There?.- How to Recognize Whether a Natural Number is a Prime.- Are There Functions Defining Prime Numbers?.- How Are the Prime Numbers Distributed?.- Which Special Kinds of Primes Have Been Considered?.- Heuristic and Probabilistic Results About Prime Numbers.
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