Prime number races

Chebyshev noticed in the first half of the nineteenth century that for any given value of x, there always seem to be more primes of the form 4n+3 less than x than there are of the form 4n+1. Similar observations have been made with primes of the form 3n+2 and 3n+1, with primes of the form 10n+3/10n+7 and 10n+1/10n+9, and many others besides. More generally, one can consider primes of the form qn+a, qn+b, qn+c, ... for our favorite constants q, a, b, c, ... and try to figure out which forms are preferred over the others. In this colloquium, we describe these phenomena in greater detail and explain the efforts that have been made at understanding them.

Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).