In the new edition of this highly successful book, Richard Crandall and Carl Pomerance have provided updated material on theoretical, computational, and algorithmic fronts, including the striking new "AKS" test for recognizing prime numbers. Other examples: new computational results on the Riemann hypothesis, a very new and superfast pure-binary algorithm for the greatest common divisor, and new forms of the fast Fourier transform. The authors also list many new computational records and survey new developments in the theory of prime numbers, including the proof that there are arbitrarily long arithmetic progressions of primes and the proof that 8 and 9 are the only consecutive powers. Numerous exercises have also been added.

About the first edition:

"It's rare to say this of a math book, but open Prime Numbers to a random page and it's hard to put down. Crandall and Pomerance have written a terrific book."

- Bulletin of the AMS

�ber die Autorin bzw. den Autor

Richard Crandall currently holds the title of Apple Distinguished Scientist, having previously been Apples Chief Cryptographer, the Chief Scientist at NeXT, Inc., and recipient of the Vollum Chair of Science at Reed College. His primary interest is interdisciplinary scientific computation, though he has authored numerous theoretical papers in quantum physics, biology, mathematics, and chemistry, as well as various patents across engineering fields.

Carl Pomerance received his Ph.D. in mathematics from Harvard University in 1972. Currently he is a professor at Dartmouth College. A popular lecturer and winner of the Chauvenet and Conant Prizes for expository mathematical writing, Pomerance is well known for his research in computational number theory, his efforts having produced important algorithms now in wide use.

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