**Date & Time:** Thursday, September 26, 2013, 11:30-12:30.

**Venue:** Ramanujan Hall

**Title:** Constant principal rank or consecutive integers with equally many
distinct prime factors

**Speaker:** Roger B. Eggleton, Illinois State University & University of Newcastle

**Abstract:** This talk will be in three parts. It is about some concrete, easily
described questions in Computational Number Theory. For the most part it will be
quite accessible to a general audience with interests in mathematics or computer
science.

In the first part, I will provide a gentle introduction to the problem, and
present a few of the classical results. In the second part, I will discuss
concrete computational results obtained jointly with Jason S. Kimberley and
James A. MacDougall, both at the University of Newcastle in Australia. In
particular, I will discuss how we obtained new lower bounds for the size of
longest runs of consecutive integers each having exactly *r* distinct prime
factors, for *3 <= r <= 63*.

In the third part, I will discuss our recent result showing that, for every *r >= 3*, there are infinitely many pairs of consecutive integers each having exactly *r* distinct prime factors.