Student Number Theory Seminar

Tristan Freiberg, Pure Mathematics, University of Waterloo

"Distribution of primes in intervals"

We discuss some conjectures, based on Cram\'er's random model, for
the distribution of primes in short intervals. We show how these
predictions are consistent with versions of the Hardy--Littlewood
prime tuples conjecture. The traditional approach is to use the
method of moments, but we use a simple inclusion-exclusion
argument, which is more explicit and could potentially lead to a
better understanding of the propagation of error terms.