Books on Prime numbers I am a graduate student and have just finished Burton's book on number theory. Now I want to read further on prime numbers. Does anyone have any suggestion?
 A: I second Martin's recommendation of Pomerance & Crandall.
On the popularizer level we have books like George P. Loweke's The Lore of Prime Numbers and David Wells's Prime Numbers: The Most Mysterious Figures in Math.
Somewhere in the middle is Ribenboim's Little Book of Bigger Primes.
On a more advanced level there are books like Fine & Rosenberger's Number Theory: An Introduction Via the Distribution of Primes and David Cox's Primes of the Form $x^2 + ny^2$: From Fermat, Class Field Theory, and Complex Multiplication. That one might be a little difficult to search for in your library's computerized catalog, plus it assumes a lot of knowledge of advanced algebra.
By the way, these are all books I have checked out from a library at one time or another. If I were you, I'd just casually browse in the vicinity of QA 240 in your university's library and 510 in your public library.
A: *

*The New Book of Prime Number Records by Paulo Ribenboim is very good and will most likely fit best to your need.

*Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire. I am currently reading this book and it is a great book which tried to explain Riemann hypothesis to a layman (with basic high school math, not even calculus) and succeeds on some level too. On the other hand it explains the connection of Riemann Hypothesis with prime numbers. Also, a great historic chapters and insights into Prime Obsession in history of Maths.

A: You could try Carl Pomerance Prime numbers, a computational Perspective.
A: Marcus du sautoy Music of the primes provides a good history and is more recreational (ie no proper theorems or proofs) but does get more technical than your average public maths book.
A: I strongly recommend Elementary Number Theory: An Algebraic Approach by Mr. Ethan Bolker. The author is sometimes active on this very site.
In general, any book about elementary number theory is sure to contain lots of theorems and proofs about prime numbers. Algebraic number theory books, too.
The book about $\sqrt{2}$ might also have some interesting material about prime numbers.
A: There is a wonderful book that just came out:
An Illustrated Theory of Numbers by Martin Weissman
It is a very interesting read and provides lots of visualizations from number theory.
