Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Products of two proportional primes   In RSA cryptography numbers of the form $pq$, with $p$ and $q$ two distinct
proportional primes play an important role. For a fixed real number $r>1$ we
formalize this by saying that an integer $pq$ is an RSA-integer if $p$ and $q$
are primes satisfying $p<q\le rp$. Recently Dummit, Granville and Kisilevsky
showed that substantially more than a quarter of the odd integers of the form
$pq$ up to $x$, with $p, q$ both prime, satisfy $p\equiv q\equiv 3\pmod{4}$. In
this paper we investigate this phenomenon for RSA-integers. We establish an
analogue of a strong form of the prime number theorem with the logarithmic
integral replaced by a variant. From this we derive an asymptotic formula for
the number of RSA-integers $\le x$ which is much more precise than an earlier
one derived by Decker and Moree in 2008.

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The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
21
The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
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The categories of this paper are: stat
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom