Although the sequence of primes is very well distributed in the reduced residue classes (mod q)(mod q), the distribution of pairs of consecutive primes among the permissible ϕ(q)2 pairs of reduced residue classes (mod q)(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 wit... read moreh numerical data, and the observed fit is very good.read less
Lemke Oliver, Robert J., and Kannan Soundararajan. "Unexpected Biases in the Distribution of Consecutive Primes." Proceedings of the National Academy of Sciences 113, no. 31 (July 14, 2016): E4446-E4454. doi:10.1073/pnas.1605366113.