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.