11 of 11 people found the following review helpful:
5.0 out of 5 stars
Great, but seriously misrepresented, January 5, 2007
This review is from: The New Book of Prime Number Records (Hardcover)
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.
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2 of 2 people found the following review helpful:
5.0 out of 5 stars
good detailed number theory book motivated by record primes, November 25, 2009
This review is from: The New Book of Prime Number Records (Hardcover)
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.
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4 of 5 people found the following review helpful:
5.0 out of 5 stars
A glorious book, April 17, 2000
This review is from: The New Book of Prime Number Records (Hardcover)
This book is a must have for anybody interested in number theory. It contains a treasure trove of solved and unsolved problems in number theory and records related to them and is highly entertaining.
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