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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 \[ L(x) = \exp \{ \log x\log \log \log x/\log \log x\} ,\] 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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Keywords: Pseudoprime, Carmichael number, Euler’s function
Article copyright: © Copyright 1981 American Mathematical Society