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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the distribution of pseudoprimes


Author: Carl Pomerance
Journal: Math. Comp. 37 (1981), 587-593
MSC: Primary 10A21; Secondary 10A20
MathSciNet review: 628717
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Abstract: Let $ \mathcal{P}(x)$ denote the pseudoprime counting function. With

$\displaystyle L(x) = \exp \{ \log x\log \log \log x/\log \log x\} ,$

we prove $ \mathcal{P}(x) \leqslant x \bullet L{(x)^{ - 1/2}}$ for large x, an improvement on the 1956 work of Erdös. We conjecture that $ \mathcal{P}(x) = x \bullet L{(x)^{ - 1 + o(1)}}$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1981-0628717-0
PII: S 0025-5718(1981)0628717-0
Keywords: Pseudoprime, Carmichael number, Euler's function
Article copyright: © Copyright 1981 American Mathematical Society