# Robert Lemke Oliver

Affiliation: Stanford University

Email: rjlo@stanford.edu

Title Of Talk: Consecutive primes modulo $q$

Abstract: The primes are well-known to be equidistributed among the admissible residue classes modulo any integer $q\geq 3$. Here, we consider the distribution of consecutive primes modulo $q$, and we find considerable deviation from the natural prediction. We offer a conjectural explanation for this deviation, and we provide a conditional proof of this conjecture. This is joint work with Kannan Soundararajan.