Classifying real Lehmer triples: a revived computation

In this article we build on the work of Schinzel cite{schinzelI}, and prove that if $n>4$, $n eq 6$, $n/(eta kappa)$ is an odd integer, and the triple $(n,alpha,eta)$, in case $(alpha-eta)^2>0$, is not equivalent to a triple $(n,alpha,eta)$ from an explicit table, then the $n$th Lehmer number $u_n(alpha, eta)$ has at least two primitive divisors.