title: Unexpected biases in the distribution of consecutive primes.
abstract: 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.
authors.affiliation: Department of Mathematics, Stanford University, Stanford, CA 94305; Department of Mathematics, Tufts University, Medford, MA 02155 robert.lemke_oliver@tufts.edu ksound@stanford.edu.
authors.forename: Robert J
authors.initials: RJ
authors.lastname: Lemke Oliver
authors.affiliation: Department of Mathematics, Stanford University, Stanford, CA 94305; robert.lemke_oliver@tufts.edu ksound@stanford.edu.
authors.forename: Kannan
authors.initials: K
authors.lastname: Soundararajan
keywords: Hardy–Littlewood conjectures; consecutive primes; prime numbers; singular series