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Journal Article

Primitive root bias for twin primes

MPS-Authors
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Luca,  Florian
Max Planck Institute for Mathematics, Max Planck Society;

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Fulltext (public)

arXiv:1705.02485.pdf
(Preprint), 602KB

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Citation

Garcia, S. R., Kahoro, E., & Luca, F. (2019). Primitive root bias for twin primes. Experimental Mathematics, 28(2), 151-160. doi:10.1080/10586458.2017.1360809.


Cite as: http://hdl.handle.net/21.11116/0000-0004-9AB6-1
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 0.459% 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.