Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounded length intervals containing two primes and an almost-prime   Goldston, Pintz and Y\i ld\i r\i m have shown that if the primes have `level
of distribution' $\theta$ for some $\theta>1/2$ then there exists a constant
$C(\theta)$, such that there are infinitely many integers $n$ for which the
interval $[n,n+C(\theta)]$ contains two primes. We show under the same
assumption that for any integer $k\ge 1$ there exists constants $D(\theta,k)$
and $r(\theta,k)$, such that there are infinitely many integers $n$ for which
the interval $[n,n+D(\theta,k)]$ contains two primes and $k$ almost-primes,
with all of the almost-primes having at most $r(\theta,k)$ prime factors. If
$\theta$ can be taken as large as $1-\epsilon$, and provided that numbers with
2, 3, or 4 prime factors also have level of distribution $1-\epsilon$, we show
that there are infinitely many integers $n$ such that the interval $[n,n+90]$
contains 2 primes and a number with at most 4 prime factors.

1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex