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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the distribution of pseudoprimes
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by Carl Pomerance PDF
Math. Comp. 37 (1981), 587-593 Request permission

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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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 587-593
  • MSC: Primary 10A21; Secondary 10A20
  • DOI: https://doi.org/10.1090/S0025-5718-1981-0628717-0
  • MathSciNet review: 628717