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 t

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 ϕ(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. - https://arxiv.org/abs/1603.03720 https://arxiv.org/abs/1603.03720