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arXiv · 1603.03720

Unexpected biases in the distribution of consecutive primes

Robert J. Lemke Oliver·Kannan Soundararajan
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Abstract

While the sequence of primes is very well distributed in the reduced residue classes (mod $q$), the distribution of pairs of consecutive primes among the permissible $\phi(q)^2$ pairs of reduced residue classes (mod $q$) is surprisingly erratic. This paper proposes a conjectural explanation for this phenomenon, based on the Hardy-Littlewood conjectures. The conjectures are then compared to numerical data, and the observed fit is very good.

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Robert J. Lemke Oliver, Kannan Soundararajan. 2016-03-11. Unexpected biases in the distribution of consecutive primes. https://doi.org/10.1073/pnas.1605366113

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