I am not familiar with all the ways the GRH can be disproven, but Miller-Rabin doesn't strike me as the most efficient, with its running time of O((log n)^4) fo

I am not familiar with all the ways the GRH can be disproven, but Miller-Rabin doesn't strike me as the most efficient, with its running time of O((log n)^4) for each attempt. I am not sufficiently competent to say whether a GRH counterexample also directly results in a MR counterexample.