Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wright's Fourth Prime   Wright proved that there exists a number $c$ such that if $g_0 = c$ and
$g_{n+1} = 2^{g_n}$, then $\lfloor g_n \rfloor$ is prime for all $n > 0$.
  Wright gave $c = 1.9287800$ as an example. This value of $c$ produces three
primes, $\lfloor g_1 \rfloor = 3$, $\lfloor g_2 \rfloor = 13$, and $\lfloor g_3
\rfloor = 16381$. But with this $c$, $\lfloor g_4 \rfloor$ is a 4932-digit
composite number. However, this slightly larger value of $c$, \[ c = 1.9287800
+ 8.2843 \cdot 10^{-4933}, \] reproduces Wright's first three primes and
generates a fourth: \[ \lfloor g_4 \rfloor = 191396642046311049840383730258
\text{ } \ldots \text{ } 303277517800273822015417418499 \] is a 4932-digit
prime.
  Moreover, the sum of the reciprocals of the primes in Wright's sequence is
transcendental.

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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: nlin