Spacings between integers having typically many prime factors

Details Spacings between integers having typically many prime factors Spacings between integers having typically many prime factors

2008-03-12

arxiv.org/abs/0803.1868v5

Mathematics

Number Theory

14 pages

Scientific paper

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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