Primes! -- Number-Theoretical Tools -- Recognizing Primes and Composites -- Primality Proving -- Exponential Factoring Algorithms -- Subexponential Factoring Algorithms -- Elliptic Curve Arithmetic -- The Ubiquity of Prime Numbers -- Fast Algorithms for Large-Integer Arithmetic.Prime numbers beckon to the beginner, as the basic notion of primality is accessible even to children. Yet, some of th…