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# Spacings Between Integers Having Typically Many Prime Factors

Published:2009-12-04
Printed: Mar 2010
• 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 $\delta$ arbitrarily small and positive, the nearest neighbor spacings between integers n with $|\omega(n) - log log n| < (log log n)^{\delta}$ obey the Poisson distribution law.
 MSC Classifications: 11K99 - None of the above, but in this section