%0 Journal Article
%T On consecutive primitive elements in a finite field
%A Stephen D. Cohen
%A Tom¨¢s Oliveira e Silva
%A Tim Trudgian
%J Mathematics
%D 2014
%I arXiv
%X For $q$ an odd prime power with $q>169$ we prove that there are always three consecutive primitive elements in the finite field $\mathbb{F}_{q}$. Indeed, there are precisely eleven values of $q \leq 169$ for which this is false. For $4\leq n \leq 8$ we present conjectures on the size of $q_{0}(n)$ such that $q>q_{0}(n)$ guarantees the existence of $n$ consecutive primitive elements in $\mathbb{F}_{q}$, provided that $\mathbb{F}_{q}$ has characteristic at least~$n$. Finally, we improve the upper bound on $q_{0}(n)$ for all $n\geq 3$.
%U http://arxiv.org/abs/1410.6210v1