On the differences between consecutive prime numbers, I

Details On the differences between consecutive prime numbers, I On the differences between consecutive prime numbers, I

2011-11-14

arxiv.org/abs/1111.3380v1

Mathematics

Number Theory

6 pages

Scientific paper

We show by an inclusion-exclusion argument that the prime $k$-tuple conjecture of Hardy and Littlewood provides an asymptotic formula for the number of consecutive prime numbers which are a specified distance apart. This refines one aspect of a theorem of Gallagher that the prime $k$-tuple conjecture implies that the prime numbers are distributed in a Poisson distribution around their average spacing.

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