Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the first sign change in Mertens' Theorem   The function $\sum_{p\leq x} \frac{1}{p} - \log\log(x) - M$ is known to
change sign infinitely often, but so far all calculated values are positive. In
this paper we prove that the first sign change occurs well before
$\exp(495.702833165)$.

30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th