Bulletin of the American Mathematical Society

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Book Information

Author(s): Hans Riesel
Title: Prime numbers and computer methods for factorization
Additional book information: Progress in Mathematics, vol. 57, Birkhäuser, Boston, Basel and Stuttgart, 1985, xvi + 464 pp., $44.95. ISBN 0-8176-3291-3

1.: L. M. Adleman, C. Pomerance and R. S. Rumely, On distinguishing prime numbers from composite numbers, Ann. of Math. 117 (1983), 173-206. MR 683806
2.: H. Cohen and A. K. Lenstra, Implementation of a new primality test, Math. Comp. 48 (1987), 103-121. MR 866102
3.: S. Goldwasser and J. Kilian, Almost all primes can be quickly certified, Proc. 18th Annual ACM Symp. on Theory of Computing (1986), 316-329.
4.: J. C. Lagarias and A. M. Odlyzko, Computing π(x): an analytic method, J. Algorithms 8 (1987), 173-191.
5.: J. C. Lagarias, V. S. Miller and A. M. Odlyzko, Computing π(x): the Meissel-Lehmer method, Math. Comp. 44 (1985), 537-560.
6.: D. H. Lehmer, Strong Carmichael numbers, J. Austral. Math. Soc. Ser. A 21 (1976), 508-510. MR 417032
7.: A. K. Lenstra and H. W. Lenstra, Jr., Algorithms in number theory, Handbook of Theoretical Computer Science (to appear).
8.: H. W. Lenstra, Jr., Factoring integers with elliptic curves, Ann. of Math. (to appear).
9.: J. M. Pollard, Theorems on factorization and primality testing, Proc. Cambridge Philos. Soc. 76 (1974), 521-528. MR 354514
10.: C. Pomerance, Analysis and comparison of some integer factoring algorithms, Computational Methods in Number Theory (H. W. Lenstra, Jr. and R. Tijdeman, eds. ), Math. Centre Tracts 154/155, Mathematisch Centrum, Amsterdam, 1982, pp. 89-139. MR 700260
11.: C. Pomerance, The quadratic sieve factoring algorithm, Advances in Cryptology (T. Beth, N. Cot and I. Ingemarsson, eds. ), Springer Lecture Notes in Computer Science 209 (1985), 169-182. MR 825590
12.: C. Pomerance, Fast, rigorous factorization and discrete logarithm algorithms, Discrete Algorithms and Complexity (D. S. Johnson, T. Nishizeki, A. Nozaki and H. S. Wilf, eds. ), Academic Press, Orlando, Florida, 1987, pp. 119-143. MR 910929
13.: M. O. Rabin, Probabilistic algorithms for testing primality, J. Number Theory 12 (1980), 128-138. MR 566880
14.: J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94. MR 137689
15.: R. J. Schoof, Elliptic curves over finite fields and the computation of square roots mod p, Math. Comp. 44 (1985), 483-494. MR 777280
16.: R. Solovay and V. Strassen, A fast Monte-Carlo test for primality, SIAM J. Comput. 6 (1977), 84-85; erratum, ibid. 7 (1978), 118. MR 429721
17.: V. Strassen, Einige Resultate über Berechnungskomplexität, Jahresber. Deutsch. Math.-Verein 78 (1976/77), 1-8. MR 438807

Review Information:
Journal: Bull. Amer. Math. Soc. 18 (1988), 61-65.
DOI: 10.1090/S0273-0979-1988-15599-1
PII: S 0273-0979(1988)15599-1

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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