Number Theory: An Introduction via the Density of Primes, Second Edition

A solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem
Concise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals
One of the few books to include the AKS algorithm that shows that primality testing is one of polynomial time
Many interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers