Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
MathSciNet review:
1567820
Full text of review:
PDF
This review is available free of charge.
Book Information:
Author:
Paulo Ribenboim
Title:
The book of prime number records
Additional book information:
Springer-Verlag, New York, Berlin, Heidelberg, 1988, xxiii + 476 pp., $49.80. ISBN 0-387-96573-4.
Richard P. Brent and Graeme L. Cohen, A new lower bound for odd perfect numbers, Math. Comp. 53 (1989), no. 187, 431–437, S7–S24. MR 968150, DOI 10.1090/S0025-5718-1989-0968150-2
John Brillhart, D. H. Lehmer, J. L. Selfridge, Bryant Tuckerman, and S. S. Wagstaff Jr., Factorizations of $b^n \pm 1$, 2nd ed., Contemporary Mathematics, vol. 22, American Mathematical Society, Providence, RI, 1988. $b=2,3,5,6,7,10,11,12$ up to high powers. MR 996414, DOI 10.1090/conm/022
Jing Run Chen, On the least prime in an arithmetical progression and theorems concerning the zeros of Dirichlet’s $L$-functions. II, Sci. Sinica 22 (1979), no. 8, 859–889. MR 549597
4. H. Dubner, Factorial and primorial primes, J. Recr. Math. 19 (1987), 197-203.
P. D. T. A. Elliott and H. Halberstam, The least prime in an arithmetic progression, Studies in Pure Mathematics (Presented to Richard Rado), Academic Press, London, 1971, pp. 59–61. MR 0272728
J. C. Lagarias, V. S. Miller, and A. M. Odlyzko, Computing $\pi (x)$: the Meissel-Lehmer method, Math. Comp. 44 (1985), no. 170, 537–560. MR 777285, DOI 10.1090/S0025-5718-1985-0777285-5
7. D. N. Lehmer, List of prime numbers from 1 to 10, 006, 721, reprinted by Hafner, New York, 1956.
Daniel Shanks, Solved and unsolved problems in number theory, 2nd ed., Chelsea Publishing Co., New York, 1978. MR 516658
Herman J. J. te Riele, Corrigenda: “On the zeros of the Riemann zeta function in the critical strip. II” [Math. Comp. 39 (1982), no. 160, 681–688; MR0669660 (83m:10067)] by R. P. Brent, J. van de Lune, te Riele and D. T. Winter, Math. Comp. 46 (1986), no. 174, 771. MR 829646, DOI 10.1090/S0025-5718-1986-0829646-4
Jeff Young and Aaron Potler, First occurrence prime gaps, Math. Comp. 52 (1989), no. 185, 221–224. MR 947470, DOI 10.1090/S0025-5718-1989-0947470-1
- 1.
- R. P. Brent and G. L. Cohen, A new lower bound for odd perfect numbers, Math. Comp. 53 (1989). MR 0968150
- 2.
- J. Brillhart, D. H. Lehmer, J. L. Selfridge, B. Tuckerman and S. S. Wagstaff, Jr., Factorizations of b ± 1, b = 2, 3, 5, 6, 7, 10, 11, 12, up to high powers, Contemporary Math., vol. 22, Amer. Math. Soc., Providence, R. I., 1983; second edition 1988. MR 996414
- 3.
- J. R. Chen, On the least prime in an arithmetical progression and theorems concerning the zeros of Dirichet's L-function. II, Sci. Sinica 22 (1979), 859-889. MR 549597
- 4.
- H. Dubner, Factorial and primorial primes, J. Recr. Math. 19 (1987), 197-203.
- 5.
- P. D. T. A. Elliott and H. Halberstam, The least prime in an arithmetic progression, Studies in Pure Mathematics (R. Rado, ed. ) Academic Press, London, 1971, pp. 59-61. MR 272728
- 6.
- J. C. Lagarias, V. S. Miller and A. M. Odlyzko, Computing $\pi(x)$: the Meissel-Lehmer method, Math. Comp. 44 (1985), 537-560. MR 777285
- 7.
- D. N. Lehmer, List of prime numbers from 1 to 10, 006, 721, reprinted by Hafner, New York, 1956.
- 8.
- D. Shanks, Solved and unsolved problems in number theory, Spartan, Washington, 1962; second edition by Chelsea, New York, 1978; third edition by Chelsea, Bronx, 1985. MR 516658
- 9.
- J. van de Lune, H. J. J. te Riele and D. T. Winter, On the zeros of the Riemann zeta function in the critical strip. IV, Math. Comp. 47 (1986), 667-681. MR 829646
- 10.
- J. Young and A. Potler, First occurrence prime gaps, Math. Comp. 52 (1989), 221-224. MR 947470
Review Information:
Reviewer:
S. S. Wagstaff, Jr.
Journal:
Bull. Amer. Math. Soc.
21 (1989), 365-369
DOI:
https://doi.org/10.1090/S0273-0979-1989-15866-7
