Infinitude conjecture for wisde primes

Let $\mathbb{P}$ be the set of primes and define the set of wisde primes by

$$\mathcal{W}=\left\{p\in\mathbb{P}:\delta(p)=\left\lfloor\sqrt[3]{\frac{p}{2}}\right\rfloor\right\}.$$

Wisde-prime infinitude conjecture. The set $\mathcal{W}$ is infinite. The paper gives computational evidence for many such primes and notes that this is equivalent to the infinitude of the set of values attained by $\delta$ on $\mathcal{W}$, but no proof is known.