The p-local lower-bound conjecture for p'-degree characters

Let $p$ be a prime, let $G$ be a finite group whose order is divisible by $p$, and let $P\in\operatorname{Syl}_p(G)$. p-local lower-bound conjecture. The number of irreducible $p'$-degree characters satisfies

$$|\operatorname{Irr}_{p'}(G)|\geq \frac{\exp(P/P')-1}{p-1}+2\sqrt{p-1}-1.$$

The source states that this conjecture follows from the continuity conjecture together with other results, and proves the bound for $p=2$; its general status is therefore open.