03533nmm a2200301 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002200139245011200161250001700273260004800290300003100338505028300369653001800652653001800670700003300688710003400721041001900755989003600774856006800810082001000878520066600888520079301554520088402347EB000354539EBX0100000000000000020759100000000000000.0cr|||||||||||||||||||||130626 ||| eng a97803872897931 aCrandall, Richard00aPrime NumbershElektronische RessourcebA Computational Perspectivecby Richard Crandall, Carl B. Pomerance a2nd ed. 2005 aNew York, NYbSpringer New Yorkc2005, 2005 aXV, 597 pbonline resource0 aPrimes! -- Number-Theoretical Tools -- Recognizing Primes and Composites -- Primality Proving -- Exponential Factoring Algorithms -- Subexponential Factoring Algorithms -- Elliptic Curve Arithmetic -- The Ubiquity of Prime Numbers -- Fast Algorithms for Large-Integer Arithmetic aNumber theory aNumber Theory1 aPomerance, Carl B.e[author]2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005- uhttps://doi.org/10.1007/0-387-28979-8?nosfx=yxVerlag3Volltext0 a512.7 aFrom the reviews of the first edition: "Destined to become a definitive textbook conveying the most modern computational ideas about prime numbers and factoring, this book will stand as an excellent reference for this kind of computation, and thus be of interest to both educators and researchers." L'Enseignement MathÃ©matique "...Prime Numbers is a welcome addition to the literature of number theory---comprehensive, up-to-date and written with style." - American Scientist "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. aRichard Crandall currently holds the title of Apple Distinguished Scientist, having previously been Apple's Chief Cryptographer, the Chief Scientist at NeXT, Inc., and recipient of the Vollum Chair of Science at Reed College. Though he publishes in quantum physics, biology, mathematics, and chemistry, and holds various engineering patents, his primary interest is interdisciplinary scientific computation. Carl Pomerance is the recipient of the Chauvenet and Conant Prizes for expository mathematical writing. He is currently a mathematics professor at Dartmouth College, having previously been at the University of Georgia and Bell Labs. A popular lecturer, he is well known for his research in computational number theory, his efforts having produced important algorithms now in use. aPrime numbers beckon to the beginner, as the basic notion of primality is accessible even to children. Yet, some of the simplest questions about primes have confounded humankind for millennia. In the new edition of this highly successful book, Richard Crandall and Carl Pomerance have provided updated material on theoretical, computational, and algorithmic fronts. New results discussed include the AKS test for recognizing primes, computational evidence for the Riemann hypothesis, a fast binary algorithm for the greatest common divisor, nonuniform fast Fourier transforms, and more. The authors also list new computational records and survey new developments in the theory of prime numbers, including the magnificent proof that there are arbitrarily long arithmetic progressions of primes, and the final resolution of the Catalan problem. Numerous exercises have been added.