Textbook in PDF format The Mystery of the Prime Numbers uses an innovative visual approach to communicate some surprisingly advanced mathematical ideas without any need for formulas or equations. The issue of prime numbers acts as a gateway into some truly strange philosophical territory whose relevance extends well beyond mathematics. An introduction Numbers and counting and how they’ve taken over the world How to build the number system: five simple rules that take you out to infinity Prime numbers: something anyone could have noticed Prime factors and the most important thing we know about numbers A philosophical interlude and a journey into space Addition versus multiplication: they’re surprisingly different things An infinity of primes: how we can be sure there isn’t a biggest one Patterns and formulas: the questions everyone seems to ask Spirals: the central image in this story The distribution: the curiously random-looking arrangement of primes Staircases: a useful way to picture the distribution The deviation: isolating the deviant behaviour of the primes Harmonic decomposition: breaking everything down into waves Spiral waves: which no one’s bothered to name properly Mysterious frequencies: the inevitable cliffhanger ending Notes Appendices