Books on Prime numbers

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.

You could try Carl Pomerance Prime numbers, a computational Perspective.

• 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.