Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unexpected biases in the distribution of consecutive primes   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 $\phi(q)^2$ 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.

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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: cond-mat