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.