3:00 p.m., Friday (November 7, 2008)
Prime number races
Abstract: This talk is a survey of "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, 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 - not to mention what,
precisely, being "preferred" means. We describe these phenomena in
greater detail and explain the efforts that have been made at
Refreshments will be served at 2:45 p.m. (Math Lounge, MATX 1115).