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On the Distribution of Pseudoprimes

Carl Pomerance
Mathematics of Computation
Vol. 37, No. 156 (Oct., 1981), pp. 587-593
DOI: 10.2307/2007448
Stable URL: http://www.jstor.org/stable/2007448
Page Count: 7
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On the Distribution of Pseudoprimes
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Abstract

Let $\mathscr{P}(x)$ denote the pseudoprime counting function. With $$L(x) = \exp\{\log x \log \log \log x/\log \log x\},$$ we prove $\mathscr{P}(x) \leqslant x \cdot L(x)^{-1/2}$ for large $x$, an improvement on the 1956 work of Erdös. We conjecture that $\mathscr{P}(x) = x \cdot L(x)^{-1 + o(1)}$.

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