Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: What is the best approach to counting primes?   As long as people have studied mathematics, they have wanted to know how many
primes there are. Getting precise answers is a notoriously difficult problem,
and the first suitable technique, due to Riemann, inspired an enormous amount
of great mathematics, the techniques and insights permeating many different
fields. In this article we will review some of the best techniques for counting
primes, centering our discussion around Riemann's seminal paper. We will go on
to discuss its limitations, and then recent efforts to replace Riemann's theory
with one that is significantly simpler.

28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org