Proving Prime Patterns
The sequence of primes begins 2, 3, 5, 7, 11, 13, 17, 19… and seems at first somewhat irregular, even random. But looking at lists of thousands of primes some patterns seem to appear, such as the persistence of twin primes (pairs of primes differing by just 2). Are there really any persistent patterns? Is there a formula for the primes?
In this talk we will review some of what is known and what most mathematicians believe but none can prove. We will also discuss some wild speculations. Finally, I will explain how to apply some of the latest and most exciting discoveries to prove that a few of the apparent patterns are indeed persistent.
Dr. Andrew Granville is the Canadian Research Chair in number theory at the Université de Montréal. He specializes in analytic number theory and properties of prime numbers. Granville is a graduate of Trinity College, University of Cambridge. He obtained his doctorate at Queen’s University, Kingston, Ontario. In 1989-91, he was a member of the Institute for Advanced Study, Princeton. Before coming to Montreal in 2002, he was a professor at the University of Georgia.