Unexpected biases in the distribution of consecutive primes.
basic_science · Level V
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- Record sourced from PubMed, PMID 27418603.
- Also identified by DOI 10.1073/pnas.1605366113 and PMC identifier 4978288.
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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.