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A CONDITIONAL DENSITY FOR CARMICHAEL NUMBERS

Published online by Cambridge University Press:  13 February 2020

THOMAS WRIGHT*
Affiliation:
429 N. Church St., Spartanburg, SC29302, USA email [email protected]

Abstract

Under sufficiently strong assumptions about the first prime in an arithmetic progression, we prove that the number of Carmichael numbers up to $X$ is $\gg X^{1-R}$, where $R=(2+o(1))\log \log \log \log X/\text{log}\log \log X$. This is close to Pomerance’s conjectured density of $X^{1-R}$ with $R=(1+o(1))\log \log \log X/\text{log}\log X$.

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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