Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On solutions of some of unsolved problems in number theory, specifically
  on the distribution of primes   We solve some famous conjectures on the distribution of primes. These
conjectures are to be listed as Legendre's, Andrica's, Oppermann's, Brocard's,
Cram\'{e}r's, Shanks', and five Smarandache's conjectures. We make use of both
Firoozbakht's conjecture (which recently proved by the author) and Kourbatov's
theorem on the distribution of and gaps between consecutive primes. These
latter conjecture and theorem play an essential role in our methods for proving
these famous conjectures. In order to prove Shanks' conjecture, we make use of
Panaitopol's asymptotic formula for $\pi(x)$ as well.

35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat