The Rabin-Monier theorem for Lucas pseudoprimes

Arnault, F.

doi:10.1090/S0025-5718-97-00836-3

The Rabin-Monier theorem for Lucas pseudoprimes
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Math. Comp. 66 (1997), 869-881 Request permission

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 $(P,Q)$.

References

F. Arnault, Rabin-Miller primality test: composite numbers which pass it, Math. Comp. 64 (1995), no. 209, 355–361. MR 1260124, DOI 10.1090/S0025-5718-1995-1260124-2
—, Constructing Carmichael numbers which are strong pseudoprimes to several bases, J. Symbolic Comput. 20 (1995), 151–161.
F. Arnault and G. Robin, Sur une fonction associée aux entiers quadratiques, Preprint.
Robert Baillie and Samuel S. Wagstaff Jr., Lucas pseudoprimes, Math. Comp. 35 (1980), no. 152, 1391–1417. MR 583518, DOI 10.1090/S0025-5718-1980-0583518-6
Gerhard Jaeschke, On strong pseudoprimes to several bases, Math. Comp. 61 (1993), no. 204, 915–926. MR 1192971, DOI 10.1090/S0025-5718-1993-1192971-8
Z. Mo and J. P. Jones, A new probabilistic primality test using Lucas sequences, Preprint.
Louis Monier, Evaluation and comparison of two efficient probabilistic primality testing algorithms, Theoret. Comput. Sci. 12 (1980), no. 1, 97–108. MR 582244, DOI 10.1016/0304-3975(80)90007-9
Carl Pomerance, J. L. Selfridge, and Samuel S. Wagstaff Jr., The pseudoprimes to $25\cdot 10^{9}$, Math. Comp. 35 (1980), no. 151, 1003–1026. MR 572872, DOI 10.1090/S0025-5718-1980-0572872-7
Michael O. Rabin, Probabilistic algorithm for testing primality, J. Number Theory 12 (1980), no. 1, 128–138. MR 566880, DOI 10.1016/0022-314X(80)90084-0
H. C. Williams, On numbers analogous to the Carmichael numbers, Canad. Math. Bull. 20 (1977), no. 1, 133–143. MR 447099, DOI 10.4153/CMB-1977-025-9