Prime-detecting sieves

Includes index

Includes bibliographical references

Chapter 1. Introduction Chapter 2. The Vaughan Identity Chapter 3. The Alternative Sieve Chapter 4. The Rosser-Iwaniec Sieve Chapter 5. Developing the Alternative Sieve Chapter 6. An Upper-Bound Sieve Chapter 7. Primes in Short Intervals Chapter 8. The Brun-Titchmarsh Theorem on Average Chapter 9. Primes in Almost All Intervals Chapter 10. Combination with the Vector Sieve Chapter 11. Generalizing to Algebraic Number Fields Chapter 12. Variations on Gaussian Primes Chapter 13. Primes of the Form x3 + 2y3 Chapter 14. Epilogue

This book seeks to describe the rapid development in recent decades of sieve methods able to detect prime numbers. The subject began with Eratosthenes in antiquity, took on new shape with Legendre's form of the sieve, was substantially reworked by Ivan M. Vinogradov and Yuri V. Linnik, but came into its own with Robert C. Vaughan and important contributions from others, notably Roger Heath-Brown and Henryk Iwaniec.