Before you can count from one to five, they turn simple arithmetic into difficult mathematics. The mysterious prime numbers, whose sequence starts 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, and goes on literally forever, have intrigued and fascinated mathematicians for twenty-five centuries. Though seemingly irregular to the point of randomness, primes are, in fact, determinate. This tantalizing mix of randomness and pattern has prompted mathematicians great and small to make complex calculations, propose elegant conjectures, and imagine ever-more prime-number patterns. While some of these speculations have proved phenomenally successful, many have failed and scores, if not hundreds, remain unresolved.

Prime Numbers: The Most Mysterious Figures in Math introduces these intriguing numbers and explores the many ways in which they combine utter simplicity with infinite depth and mystery. This comprehensive A-to-Z guide captures the strange attraction of primes that has entranced great minds for millennia and explains the roles that they have played in everything from Pythagorean triangles to public key cryptography.

Well-known mathematics author David Wells offers clear explanations of such fascinating concepts as the Fermat and Fibonacci numbers, Goldbach's last conjecture, the Mersenne primes, Agrawal's breakthrough "Primes is in P" algorithm—which was downloaded 30,000 times in the first twenty-four hours after it was posted on the Internet—and the celebrated Riemann hypothesis, by common consent the outstanding unsolved problem in the whole of mathematics.

As compelling as the prime numbers themselves are Wells's engaging profiles of prime-obsessed mathematicians, including Paul Erd''os, who offered rewards up to $25,000 to anyone who could prove or disprove conjectures that he posed; Leonhard Euler, who demolished Fermat's conjecture that all Fermat numbers are prime; and Srinivasa Ramanujan, who said, "An equation has for me no meaning unless it expresses a thought of God."

Packed with prime curios and challenging problems, Prime Numbers will intrigue the serious mathematician, the dedicated amateur, and the curious newcomer alike.

Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers? What did Albert Wilansky find so fascinating about his brother-in-law's phone number?

Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions. In Prime Numbers: The Most Mysterious Figures in Math, you'll meet the world's most gifted mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd?o?s, and you'll discover a host of unique insights and inventive conjectures that have both enlarged our understanding and deepened the mystique of prime numbers. This comprehensive, A-to-Z guide covers everything you ever wanted to know--and much more that you never suspected--about prime numbers, including: The unproven Riemann hypothesis and the power of the zeta functionThe ""Primes is in P"" algorithmThe sieve of Eratosthenes of CyreneFermat and Fibonacci numbersThe Great Internet Mersenne Prime SearchAnd much, much more