People with interest in number theory might be interested in this:
This book is available for free and can be downloaded from this web page. We expect the book to be completed by December 2008. In the meanwhile, you are welcome to check our progress, add ideas and suggestions (in LaTeX format) and distribute or use this resource for your own needs. It is quite possibly the first time that a mathematical book with state-of-the-art research results about fundamental - yet very deep number theoretical problems - can be accessed, and even modified, while it is in the process of being written.
The book, essentially written by Dr. Vincent Granville, is intended to a wide audience, so we want to use a terminology that many people are familiar with. So, while we occasionally make reference to facts that are very difficult to prove (e.g. about the distribution of sums of squares or prime numbers), our approach is essentially elementary, and based on combinatorics and probability theory more so than on properties of integers (congruences) or classical analytical number theory. We want this book to show to many people the beauty of mathematics and the incredible complexity of fundamental problems, such as every even integer greater than 5 can be expressed as the sum of two primes.