The Life of Primes in 37 Episodes

Book excerpt: This book is about the life of primes. Indeed, once they are defined, primes take on a life of their own and the mysteries surrounding them begin multiplying, just like living cells reproduce themselves, and there seems to be no end to it. This monograph takes the reader on a journey through time, providing an accessible overview of the numerous prime number theory problems that mathematicians have been working on since Euclid. Topics are presented in chronological order as episodes. These include results on the distribution of primes, from the most elementary to the proof of the famous prime number theorem. The book also covers various primality tests and factorisation algorithms. It is then shown how our inability to factor large integers has allowed mathematicians to create today's most secure encryption method. Computer science buffs may be tempted to tackle some of the many open problems appearing in the episodes. Throughout the presentation, the human side of mathematics is displayed through short biographies that give a glimpse of the lives of the people who contributed to the life of primes. Each of the 37 episodes concludes with a series of problems (many with solutions) that will assist the reader in gaining a better understanding of the theory.