Gaps between prime divisors and analogues in Diophantine geometry
Abstract
Erdos 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 Qp-point on a random variety are Poisson distributed.
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