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Prime Numbers

A Computational Perspective

  • Richard Crandall
  • Carl Pomerance

Table of contents

  1. Front Matter
    Pages i-xv
  2. Richard Crandall, Carl Pomerance
    Pages 1-76
  3. Richard Crandall, Carl Pomerance
    Pages 77-108
  4. Richard Crandall, Carl Pomerance
    Pages 109-158
  5. Richard Crandall, Carl Pomerance
    Pages 159-190
  6. Richard Crandall, Carl Pomerance
    Pages 191-225
  7. Richard Crandall, Carl Pomerance
    Pages 227-283
  8. Richard Crandall, Carl Pomerance
    Pages 285-351
  9. Richard Crandall, Carl Pomerance
    Pages 353-406
  10. Richard Crandall, Carl Pomerance
    Pages 407-496
  11. Back Matter
    Pages 497-547

About this book

Introduction

In this volume we have endeavored to provide a middle ground-hopefully even a bridge-between "theory" and "experiment" in the matter of prime numbers. Of course, we speak of number theory and computer experiment. There are great books on the abstract properties of prime numbers. Each of us working in the field enjoys his or her favorite classics. But the experimental side is relatively new. Even though it can be forcefully put that computer science is by no means young, as there have arguably been four or five computer "revolutions" by now, it is the case that the theoretical underpinnings of prime numbers go back centuries, even millennia. So, we believe that there is room for treatises based on the celebrated classical ideas, yet authored from a modern computational perspective. Design and scope of this book The book combines the essentially complementary areas of expertise of the two authors. (One author (RC) is more the computationalist, the other (CP) more the theorist. ) The opening chapters are in a theoretical vein, even though some explicit algorithms are laid out therein, while heavier algorithmic concentration is evident as the reader moves well into the book. Whether in theoretical or computational writing mode, we have tried to provide the most up-to-date aspects of prime-number study. What we do not do is sound the very bottom of every aspect.

Keywords

Mersenne prime Riemann zeta function Scope Volume analytic number theory arithmetic bridge calculus computer cryptography elliptic curve finite field number theory prime number zeta function

Authors and affiliations

  • Richard Crandall
    • 1
  • Carl Pomerance
    • 2
  1. 1.Center for Advanced ComputationPortlandUSA
  2. 2.Department of MathematicsDartmouth UniversityHanoverUSA

Bibliographic information