This book makes a substantial contribution to the understanding of a murky area of number theory that is important to computer science, an area relevant to the design and analysis of number-theoretic algorithms and to the construction of cryptographic protocols. Contents:Introduction; 1: Explicit Bounds for Primality Testing; Ankeny's Theorem and its Algorithmic Consequences; Background from Analytic Number Theory; Roots; Asymptotic Theorems; Zeta-function...