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Prime Numbers: A Computational Perspective, Second Edition

Richard E. Crandall
Organization: Center for Advanced Computation
Carl Pomerance
Organization: Dartmouth College
Department: Mathematics
Book information

Publisher: Springer Science+Business Media (New York)
Copyright year: 2005
ISBN: 0387252827
Medium: Hardcover
Pages: 597
Out of print?: N
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Book cover image

Primes! | 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 | Appendix: Book Pseudocode

This book is a reference for professionals and students interested in prime numbers and encryption, cryptography, factoring algorithms, elliptic curve arithmetic, and many more computational issues related to primes and factoring. The text focuses on the computational aspects of finding, testing, and characterizing prime numbers, and discusses theoretically interesting, aesthetic and practical aspects of primes.

The text provides theoretical explanations for the practical power of the computational algorithms, along with detailed pseudocode and exercises are designed to keep students engaged and interested. This second edition provides updated material on theoretical, computational, and algorithmic fronts.

Mathematica notebook implementations of all algorithms in this book are available.

*Mathematics > Number Theory
*Mathematics > Recreational Mathematics

AMC conjecture, abelian group, additive number theory, Algorithm D, analytic number theory, Artin conjecture, Atkin-Bernstein theorem, baby-steps giant-steps method, Barrett method, Berlekamp algorithm, Berlekamp-Massey algorithm, Bertrand postulate, binary segmentation, binary quadratic forms, Bluestein trick, Blum integers, Brent parameterization, Brillhart-Morrtison method, Brun-Titchmarsh inequality, Carmichael numbers, Cauchy-Schwarz inequality, Chebotarev density theorem, Chebyshev density theorem, Chinese remainder theorem, collateralized mortgage obligation, commutatative ring, cryptography, Cullen numbers, Cunningham numbers, Danielson-Lanczos identity, Deuring theorem, Diffie-Hellman key exchange, discrepancy theory, extended Riemann hypothesis, Lenstra ECM, Pollard-Strassen, number field sieve, quadratic sieve, special number field sieve, fast ECPP, Faure sequence, Galway functions, Ganhi formula, Garner algorithm, generalized Riemann hypothesis, Goldbach conjecture, Granville identity, Gray code, Halton sequence, Hasse theorem, Hensel lifting, irrational-base discrete weighted transform, Karatsuba method, Lucas-Lehmer test, McIntosh-Wagstaff probable prime, Mersenne primes, Mersenne numbers, Mertens conjecture, Montgomery coordinates, number-theoretical transform methods, perfect number, Pocklington theorem, Polya-Vinogradov inequality, powering ladders, primality testing, prime k-tuples conjecture, prime number theorem, pseudoprime, quantum Turing machine, RSA challenge, Schoof algorithm, Schoof-Elkies, Atkin variant, SHA-1 hash function, Shanks-Mestre method, Shor algorithm, Shoup method, smooth numbers, Sorenson method, Toom-Cook method, twin-prime pairs, twist curve, Vinogradov equidistribution theorem, Walsh-Hadamard transform, Weierstrass equations, Wieferich primes, Wilson primes, Wilson-Lagrange theorem
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