The New Book of Prime Number Records (Computers and Medicine) 3rd Edition by Paulo Ribenboim (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review Third EditionP. RibenboimThe New Book of Prime Number Records”A number-theoretical version of the Guinness Book of Records . . . There is much mathematics to be found in these pages. These are records given here as well. This book is written with much wit. Experts may not find much that is new, but it is always worthwhile to view the history of a subject as a whole rather than a collection of isolated results.”―MATHEMATICAL REVIEWS From the Back Cover The Guinness Book made records immensely popular. This book is devoted, at first glance, to present records concerning prime numbers. But it is much more. It explores the interface between computations and the theory of prime numbers. The book contains an up-to-date historical presentation of the main problems about prime numbers, as well as many fascinating topics, including primality testing. It is written in a language without secrets and is thoroughly accessible to everyone with some mathematical education. This new book has an improved and smoother presentation.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Ribenboim wrote a book called the Little Book of Big Primes which came out in 1991 and was written for general audiences. This book and the revised edition of the Little book are of personal interest to me because my father’s work in 1939 gets cited a lot with respect to the Carmichael numbers. This motivates me to read through the book in more detail that some of the other reviewers. But as Cube Boy mentioned this is not just about records. It is fundamentally an advanced book on number theory for mathematicians with many of the same topics as are in the Little Book but at a hogher level with more mathematical detail and with new results that came about between 1991 and 1996. I have also reviewed the second edition of the Little Book and I comment more about the prime records and my father’s contributions there. Also the second edition in 2004 has new records as the computer is able to verify that larger and larger numbers are prime.

⭐This is a fascinating and arguably essential book for mathematically-sophisticated people who want a rigorous overview of prime numbers and related aspects of number theory. It’s widely cited in other books, which is how I found it.The title sounds like it’s just a book about the largest prime numbers, but it’s far, far more than that, including proofs of virtually all prime number theorems, a great many algorithms for generating primes, computational aspects of generating and testing primes, cryptographic applications, and much more.The author is a skilled mathematician who is able to write about advanced mathematics in a remarkably clear, even jovial style.However: the Amazon description says it is “thoroughly accessible to everyone”. Utter nonsense.This quote is actually a truncated version of one on the back of the book, which says it is “…thoroughly accessible to everyone with some mathematical education”.Well, “thoroughly accessible” and “some mathematical education” are relative terms. If you think it means you will understand this book if you took 3 or 4 years of high school math — algebra, geometry, trig, pre-calculus — you will be rudely shocked. Even a year or two of college math classes may be insufficient.While you don’t necessarily need an undergraduate degree in mathematics to appreciate this book, it wouldn’t hurt — it’s used in graduate math courses.But if you have the interest, and sufficient background, you should definitely buy this book. And by all means, consider a used copy — I paid about $20 and it was fine. I think the large number of (barely) used copies available on Amazon has something to do with the number of people who bought it without realizing what they were getting into. If you have the requisite background, you would not let this book go.

⭐I’ve given this book 5 stars without ever having laid eyes on an actual copy or held one in my hand, for the following reasons:(1) I looked at pages from this book with Amazon’s viewer , and saw an impressive table of contents, an impressive excerpt from the first few pages, and an IMPRESSIVE bibliography of about 76 pages!(2) The two earlier reviewers who seemed to know what the material entails, and who (I presume) had actually read the book, gave it 5 stars.(3) I came to Amazon’s listing of this book because I had seen SO MANY references to it from other authors who were knowledgeable in this field, both in their books and in articles on the Web.I don’t usually review works I haven’t read, but felt I had to add my two cents worth to this discussion after I read the trash contained in the review by the person who obviously has no mathematical talent, said as much, and then proceeded to pan the book based on what are either outright misconceptions or metaphysical ramblings. I’ve got my doubts that he actually read that much of it either! I felt compelled to right the wrong done by his low rating. The funny thing, his rating would have applied to ANY OTHER book on this subject written by a competent person.For what it’s worth, I’m a college-level math instructor, have a master’s degree in math, have interest in this subject but don’t specialize in it, would like a copy of this book (as well as a whole lot of other books), but on my limited book budget I’m going to hold off until I can find a much cheaper used copy (as one reviewer implied were available, though I didn’t see such a bargain on the current listings).

⭐Libro molto completo e curato. Uno dei migliori che si possono trovare sull’argomento per la quantità di dettagli. Quello che più apprezzo è che non sia un libro divulgativo, senza il corretto rigore matematico: vi sono riportate le dimostrazioni dei teoremi ed usa il linguaggio e la notazione matematica. Questo certo non lo rende adatto per chi vuole solo delle informazioni di massima o degli aneddoti sui numeri primi.

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