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arXiv · 0803.1868

Spacings between integers having typically many prime factors

Rizwanur Khan
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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 $\de$ arbitrarily small and positive, the nearest neighbor spacings between integers $n$ with $|\om(n)-\log_2 n|\le (\log_2 n)^{\de}$ obey the Poisson distribution law.

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Rizwanur Khan. 2008-03-12. Spacings between integers having typically many prime factors. https://doi.org/10.4153/cmb-2010-022-8

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