Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Infinitude of Primes of the Form $b^2 + 1$   If b^2 + 1 is prime then b must be even, hence we examine the form 4u^2 + 1.
Rather than study primes of this form we study composites where the main
theorem of this paper establishes that if 4u^2 + 1 is composite, then u belongs
to a set whose elements are those u such that u^2 + t^2 = n(n + 1), where t has
a upper bound determined by the value of u. This connects the composites of the
form 4u^2 + 1 with numbers expressible as the sum of two squares equal to the
product of two consecutive integers. A result obtained by Gauss concerning the
average number of representations of a number as the sum of two squares is then
used to show that an infinite sequence of u for which u^2 + t^2 = n(n + 1) is
impossible. This entails the impossibility of an infinite sequence of
composites, and hence an infinitude of primes of the form b^2 + 1.

27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci