The meridional rank versus bridge number conjecture

Let $K$ be a knot, let $E(K)$ be its exterior, and let the meridional rank of $\pi_1(E(K))$ mean the minimum number of generators that are meridians of $K$. Let $b(K)$ denote the bridge number of $K$.

Meridional rank versus bridge number conjecture. The minimum number of meridional generators of $\pi_1(E(K))$ is equal to

$$b(K).$$

The conjecture is known for several classes, including $2$-bridge, Montesinos, torus, and certain cable knots, but remains unresolved in general.