Mathematics of Computation

Author(s): F. Arnault.
Journal: Math. Comp. 66 (1997), 869-881.
MSC (1991): Primary 11Y11; Secondary 11A51, 11R11
Retrieve article in: PDF
This article is available free of charge

Abstract: We give bounds on the number of pairs $(P,Q)$

with $0\le P,Q<n$ such that a composite number $n$

is a strong Lucas pseudoprime with respect to the parameters $(P,Q)$

1.: F. Arnault, Rabin-Miller primality test: Composite numbers which pass it, Math. Comp. 64 (1995), 355-361. MR 95c:11152
2.: -, Constructing Carmichael numbers which are strong pseudoprimes to several bases, J. Symbolic Comput. 20 (1995), 151-161. CMP 96:08
3.: F. Arnault and G. Robin, Sur une fonction associée aux entiers quadratiques, Preprint.
4.: R. Baillie and S. Wagstaff, Jr., Lucas pseudoprimes, Math. Comp. 35 (1980), 1391-1417. MR 81j:10005
5.: G. Jaeschke, On strong pseudoprimes to several bases, Math. Comp. 61 (1993), 915-926. MR 94d:11004
6.: Z. Mo and J. P. Jones, A new probabilistic primality test using Lucas sequences, Preprint.
7.: L. Monier, Evaluation and comparison of two efficient primality testing algorithms, Theoret. Comput. Sci. 11 (1980), 97-108. MR 82a:68078
8.: C. Pomerance, J. L. Selfridge, and S. S. Wagstraff, The pseudoprimes to $25\cdot 10^9$ , Math. Comp. 35 (1980), 1003-1026. MR 82g:10030
9.: M. O. Rabin, Probabilistic algorithms for testing primality, J. Number Theory 12 (1980), 128-138. MR 81f:10003
10.: H. C. Williams, On numbers analogous to the Carmichael numbers, Canad. Math. Bull. 20 (1977), 133-143. MR 56:5414

Retrieve articles in Mathematics of Computation with MSC (1991): 11Y11, 11A51, 11R11

F. Arnault
Affiliation: Université de Limoges, Faculté des Sciences, URA 1586, Laboratoire d'Arithmétique de Calcul formel et d'Optimisation, 123, av Albert Thomas, 87060 Limoges Cedex, France
Email: arnault@unilim.fr

DOI: 10.1090/S0025-5718-97-00836-3
PII: S 0025-5718(97)00836-3
Keywords: Primality testing, Lucas pseudoprimes.
Received by editor(s): August 30, 1994
Received by editor(s) in revised form: February 28, 1995 and November 6, 1995
Copyright of article: Copyright 1997, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6842(e) ISSN 0025-5718(p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS