Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some experiments with integral Apollonian circle packings   Bounded Apollonian circle packings (ACP's) are constructed by repeatedly
inscribing circles into the triangular interstices of a configuration of four
mutually tangent circles, one of which is internally tangent to the other
three. If the original four circles have integer curvature, all of the circles
in the packing will have integer curvature as well. In \cite{ll}, Sarnak proves
that there are infinitely many circles of prime curvature and infinitely many
pairs of tangent circles of prime curvature in a primitive integral ACP. In
this paper, we give a heuristic backed up by numerical data for the number of
circles of prime curvature less than $x$, and the number of "kissing primes,"
or {\it pairs} of circles of prime curvature less than $x$ in a primitive
integral ACP. We also provide experimental evidence towards a local to global
principle for the curvatures in a primitive integral ACPs.

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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con