Brignall's prime bound conjecture for graphs

Let $G$ be a graph with $|V(G)|\geq 2$. The prime bound $p(G)$ is the smallest integer such that $G$ admits a prime $p(G)$-extension; here $\alpha(G)$ denotes the stability number and $\omega(G)$ the clique number. Brignall's prime bound conjecture.

$$p(G)\leq\left\lceil\log_2\bigl(\max(\alpha(G),\omega(G))+1\bigr)\right\rceil.$$

This would improve the general upper bound obtained from the number of vertices by replacing $|V(G)|$ with the larger of the stability and clique numbers. The supplied source does not state whether the conjecture has been resolved.