Gaps between prime divisors and analogues in Diophantine geometry

Abstract

Erdős considered the second moment of the gap-counting function of prime divisors in 1946 and proved an upper bound that is not of the right order of magnitude. We prove asymptotics for all moments. Furthermore, we prove a generalisation stating that the gaps between primes $p$ for which there is no ${\mathbb{Q}}_p$-point on a random variety are Poisson distributed.

arXiv commentAdded analogues in Diophantine geometry