Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analog of the Skewes number for twin primes   The results of the computer investigation of the sign changes of the
difference between the number of twin primes $\pi_2(x)$ and the
Hardy--Littlewood conjecture $c_2\Li_2(x)$ are reported. It turns out that
$\pi_2(x) - c_2\Li_2(x)$ changes the sign at unexpectedly low values of $x$ and
for $x<2^{42}$ there are over 90000 sign changes of this difference. It is
conjectured that the number of sign changes of $\pi_2(x) - c_2\Li_2(x)$ for
$x\in (1, T)$ is given by $\sqrt T/\log(T)$.

20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org