Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Primes in the Interval [3n, 4n]   For the old question whether there is always a prime in the interval [kn,
(k+1)n] or not, the famous Bertrand's postulate gave an affirmative answer for
k=1. It was first proved by P.L. Chebyshev in 1850, and an elegant elementary
proof was given by P. Erdos in 1932. M. El Bachraoui used elementary techniques
to prove the case k=2 in 2006. This paper gives a proof of the case k=3, again
without using the prime number theorem or any deep analytic result. In addition
we give a lower bound for the number of primes in the interval [3n, 4n], which
shows that as n tends to infinity, the number of primes in the interval [3n,
4n] goes to infinity.

10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex