Large prime gaps and progressions with few primes

Abstract

We show that the existence of arithmetic progressions with few primes, with a quantitative bound on "few", implies the existence of larger gaps between primes less than x than is currently known unconditionally. In particular, we derive this conclusion if there are certain types of exceptional zeros of Dirichlet L-functions.

re-organized the description of the corollaries; typos corrected

References in corpus (1)

• Large prime gaps and probabilistic models

Cited by in corpus (2)

• Large prime gaps and probabilistic models
• Prime Tuples and Siegel Zeros