Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new bound for the smallest $x$ with $\pi(x) > li(x)$   We reduce the leading term in Lehman's theorem. This improved estimate allows
us to refine the main theorem of Bays and Hudson. Entering $2,000,000$ Riemann
zeros, we prove that there exists $x$ in the interval $[exp(727.951858),
exp(727.952178)]$ for which $\pi(x)-\li(x) > 3.2 \times 10^{151}$. There are at
least $10^{154}$ successive integers $x$ in this interval for which
$\pi(x)>\li(x)$. This interval is strictly a sub-interval of the interval in
Bays and Hudson, and is narrower by a factor of about 12.

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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph