Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost primes in almost all very short intervals   We show that as soon as $h\to \infty$ with $X \to \infty$, almost all
intervals $(x-h\log X, x]$ with $x \in (X/2, X]$ contain a product of at most
two primes. In the proof we use Richert's weighted sieve, with the arithmetic
information eventually coming from results of Deshouillers and Iwaniec on
averages of Kloosterman sums.

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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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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: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: eess