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arXiv · 2101.08038

Infinitely many twin prime polynomials of odd degree

Claire Burrin·Matthew Issac
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Abstract

While the twin prime conjecture is still famously open, it holds true in the setting of finite fields: There are infinitely many pairs of monic irreducible polynomials over $\mathbb{F}_q$ that differ by a fixed constant, for each $q \geq 3$. Elementary, constructive proofs were given for different cases by Hall and Pollack. In the same spirit, we discuss the construction of a further infinite family of twin prime tuples of odd degree, and its relations to the existence of certain Wieferich primes and to arithmetic properties of the combinatorial Bell numbers.

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Claire Burrin, Matthew Issac. 2021-01-20. Infinitely many twin prime polynomials of odd degree. https://doi.org/10.1080/00029890.2021.1981738

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