Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twins almost prime under a Elliott-Halberstam's conjecture   We improve Bombieri's asymptotic sieve to localise the variables. As a
consequence, we prove, under a Elliott-Halberstam conjecture, that there exists
an infinity of twins almost prime. Those are prime numbers $p$ such that for
all $\varepsilon>0$, $p-2$ is either a prime number or can be written as $p_1
p_2$ where $p_1$ and $p_2$ are prime and $p_1<X^{\varepsilon}$, and we give the
explicit asymptotic.

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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph