next up previous contents
Next: About this document ... Up: Primos de Mersenne (e Previous: Tabelas

Referências

[APR], L. M. Adleman, C. Pomerance e R. S. Rumely, On distinguishing prime numbers from composite numbers, Ann. Math. (2) 117 (1983) 173-206.

[AGP], W. R. Alford, A. Granville e C. Pomerance, There are infinitely many Carmichael numbers, Ann. of Math., 140 (1994) 703-722.

[Bach] Eric Bach, Explicit bounds for primality testing and related problems, Math. of Comp. 55, 1990, pp. 355-380.

[BCR], R. P. Brent, G. L. Cohen e H. J. J. te Riele, Improved techniques for lower bounds for odd perfect numbers, Math. Comp., 57 (1991) 857-868 (MR 92c:11004).

[BLS], J. Brillhart, D. H. Lehmer e J. L. Selfridge, New primality criteria and factorizations of $2m \pm 1$, Math. Comp., 29 (1975) 620-647.

[Bruce], J. W. Bruce, A really trivial proof of the Lucas-Lehmer test, Amer. Math. Monthly, April (1993) 370-371.

[Cipolla], M. Cipolla, Sui numeri composti P, che verificano la congruenza di Fermat $a^{P-1} \equiv 1 \pmod P$, Annali di Matematica, (3), 9, 1904, 139-160.

[CB], M. Clausen e U. Baum, Fast Fourier Transforms, BI-Wiss.-Verl., 1993.

[CF], R. Crandall e B. Fagin, Discrete weighted transforms and large-integer arithmetic, Math. Comp., 62:205 (1994) 305-324.

[Erdös], Paul Erdös, On a new method in elementary number theory which leads to an elementary proof of the prime number theorem, Proc. Nat. Acad. Sci. (Washington) 35 (1949) 374-384.

[EP], Paul Erdös e Carl Pomerance, On the number of false witnesses for a composite number, Math. Comp., 46 (1986) 259-279.

[GK], S. Goldwasser e J. Kilian, Almost all primes can be quickly certified, Proc. 18th STOC (Berkeley, May 28-30, 1986), ACM, New York, 1986, 316-329.

[Guy], Richard K. Guy, Unsolved Problems in Number Theory, Springer-Verlag, New York, 1994 (QA241.G87, ISBN 3-540-94289-0).

[HW], G. H. Hardy e E. M. Wright, An Introduction to the Theory of Numbers 5e, Oxford University Press, 1979.

[KP], Su Hee Kim e Carl Pomerance, The probability that a random probable prime is composite, Math. Comp., 53:188 (1989) 721-741.

[Lehmer], Derrick H. Lehmer, An extended theory of Lucas' functions, Ann. Math. 31 (1930) 419-448. Reprinted in Selected Papers (ed. D. McCarthy), Vol 1, Ch. Babbage Res. Center, St. Pierre, Manitoba Canada, 11-48, 1981.

[Lucas], E. Lucas, Théorie des fonctions numériques simplement périodiques, Amer. J. Math., 1, 1878, 184-240 e 289-321.

[Maier], H. Maier, Primes in short intervals, Michigan math. J., 32 (1985) 221-225.

[Mills], W. H. Mills, A prime representing function, Bull. Amer. Math. Soc., 53 604.

[Mollin], R. A. Mollin, Prime-producing polynomials, Amer. Math. Monthly 104 (June-July 1997) 529-544.

[Pintz], János Pintz, Very large gaps between consecutive primes, J. Number Theory 63 (1997), no. 2, 286-301.

[PSW], C. Pomerance, J. L. Selfridge e S. S. Wagstaff Jr., The pseudoprimes to 25.109, Math. Comp., 35 (1980) 1003-1026.

[Pomerance], C. Pomerance, A new lower bound for the pseudoprimes counting function, Illinois J. Math, 26, 1982, 4-9.

[Ribenboim95], P. Ribenboim, The New Book of Prime Number Records, 3ed., Springer-Verlag New York, 1995 (QA246 .R47 ISBN 0-387-94457-5).

[Ribenboim97], P. Ribenboim, Vendendo primos, Rev. Mat. Univ., 22/23, 1997, 1-13 (tradução de Selling primes, Math. Mag., 68 (1995) 175-182).

[Riesel56], H. Riesel, Naagra stora primtal (Sueco: Alguns primos grandes), Elementa 39 (1956) 258-260.

[Riesel94], H. Riesel, Prime Numbers and Computer Methods for Factorization, Progress in Mathematics, Birkhauser Boston, vol. 57, 1985; and vol. 126, 1994.

[Selberg], A. Selberg, An elementary proof of the prime number theorem, Annals of Math. 50 (1949) 305-13.

[Sierpinski], W. Sierpinski, Sur un problème concernant les nombres $k \cdot 2n+1$, Elem. Math., 15 (1960) 73-74. Corrigendum: Elem. Math., 17 (1963) 85.

[Westzynthius], E. Westzynthius, Über die Verteilung der Zahlen die zu den n ersten Primzahlen teilerfremd sind, Comm. Phys. math. Helsingfors, 5:5 (1931) 1-37.

[Wilf], H. Wilf, What is an answer? Am. Math. Monthly, 89 (1982), 289-292.

[WD], H. C. Williams e H. Dubner, The primality of R1031, Math. Comp., 47 (1986) 703-711.

[YP], J. Young e A. Potler, First occurence of primes gaps, Math. Comp., 52 (1989) 221-224.


next up previous contents
Next: About this document ... Up: Primos de Mersenne (e Previous: Tabelas
Nicolau C. Saldanha
1999-08-09