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Mathematics of Computation

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The distribution of Lucas and elliptic pseudoprimes

Authors: Daniel M. Gordon and Carl Pomerance
Journal: Math. Comp. 57 (1991), 825-838
MSC: Primary 11N80; Secondary 11B39, 11G05, 11Y11
Corrigendum: Math. Comp. 60 (1993), 877.
Corrigendum: Math. Comp. 60 (1993), 877.
MathSciNet review: 1094951
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Abstract: Let $ \mathcal{L}(x)$ denote the counting function for Lucas pseudoprimes, and $ \mathcal{E}(x)$ denote the elliptic pseudoprime counting function. We prove that, for large x, $ \mathcal{L}(x) \leq xL{(x)^{ - 1/2}}$ and $ \mathcal{E}(x) \leq xL{(x)^{ - 1/3}}$, where

$\displaystyle L(x) = \exp (\log x\log \log \log x/\log \log x).$

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Article copyright: © Copyright 1991 American Mathematical Society