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Spacings Between Integers Having Typically Many Prime Factors
Published online by Cambridge University Press: 20 November 2018
Abstract
We show that the sequence of integers which have nearly the typical number of distinct prime factors forms a Poisson process. More precisely, for $\delta$ arbitrarily small and positive, the nearest neighbor spacings between integers $n$ with $\left| \omega \left( n \right)\,-\,\log \log n \right|\,<\,{{\left( \log \log n \right)}^{\delta }}$ obey the Poisson distribution law.
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- Copyright © Canadian Mathematical Society 2010
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