Unexpected biases in the distribution of consecutive primes. - Lemke Oliver, Robert J.; Soundararajan, Kannan. (Tufts University. Tisch Library., 2017)
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 with numerical data, and the observed fit is very good.