Unexpected biases in the distribution of consecutive primes
Number Theory
2022-04-27 v4
Abstract
While the sequence of primes is very well distributed in the reduced residue classes (mod ), the distribution of pairs of consecutive primes among the permissible pairs of reduced residue classes (mod ) 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.
Keywords
Cite
@article{arxiv.1603.03720,
title = {Unexpected biases in the distribution of consecutive primes},
author = {Robert J. Lemke Oliver and Kannan Soundararajan},
journal= {arXiv preprint arXiv:1603.03720},
year = {2022}
}
Comments
v4: Added dedication v3: Minor revisions to exposition, fixed one typo in Section 5 v2: Added references