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arXiv · 1705.02485

Primitive root bias for twin primes

Stephan Ramon Garcia·Elvis Kahoro·Florian Luca
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Abstract

Numerical evidence suggests that for only about $2\%$ of pairs $p,p+2$ of twin primes, $p+2$ has more primitive roots than does $p$. If this occurs, we say that $p$ is exceptional (there are only two exceptional pairs with $5 \leq p \leq 10{,}000$). Assuming the Bateman-Horn conjecture, we prove that at least $0.47\%$ of twin prime pairs are exceptional and at least $65.13\%$ are not exceptional. We also conjecture a precise formula for the proportion of exceptional twin primes.

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Stephan Ramon Garcia, Elvis Kahoro, Florian Luca. 2017-05-06. Primitive root bias for twin primes. https://arxiv.org/abs/1705.02485

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