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- R. Crandall and C. Pomerance, Prime numbers: a computational perspective, Springer-Verlag, New York, NY, 2001. pp. xvi+545, ISBN 0-387-94777-9. MR 2002a:11007
[From the preface:] 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 experiment side is relatively new. Even though it can be forcefully put that computer science is by no means young, as there have been arguably been four or five computer "revolutions" by now, it is the case that the theoretical underpinings 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.
[This is a valuable text written by true experts in two different areas: computational and theoretical respectively. There is now a second edition [CP2005].]