Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the 'building blocks' of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no-one has ever been able to resolve them.

What is number theory? --Multiplying and dividing -- Prime-time mathematics -- Congruences, clocks, and calendars -- More triangles and squares -- From cards to cryptography -- Conjectures and theorems -- How to win a million dollars.