Matthews' generalized primitive-root conjecture

Let $a_1,a_2,\dots,a_n$ be nonzero integers other than $\pm1$, and let $A(a_1,\dots,a_n)$ denote the associated constant. For $x\in\mathbb{N}$, the number of primes not exceeding $x$ is asymptotically

$$\frac{x}{\log x}A(a_1,\dots,a_n)+O\left(\frac{x}{\log^2 x}(\log\log x)^{2^n-1}\right).$$

Matthews' generalized conjecture. The displayed asymptotic holds for the number of primes $\le x$. The source introduces this as a generalized version of Artin's conjecture and uses it in the study of normal numbers; no resolution status is supplied in the paper excerpt.