Unexpected biases in the distribution of consecutive primes.

@article{Oliver2016UnexpectedBI,
title={Unexpected biases in the distribution of consecutive primes.},
author={Robert J Lemke Oliver and K. Soundararajan},
journal={Proceedings of the National Academy of Sciences of the United States of America},
year={2016},
volume={113 31},
pages={E4446-54}
}

Although the sequence of primes is very well distributed in the reduced residue classes [Formula: see text], the distribution of pairs of consecutive primes among the permissible ϕ(q)(2) pairs of reduced residue classes [Formula: see text] is surprisingly erratic. This paper proposes a conjectural explanation for this phenomenon, based on the Hardy-Littlewood conjectures. The conjectures are then compared with numerical data, and the observed fit is very good.