The prime-minus-one sum-product conjecture

Write $\mathbb{P}$ for the set of primes. Prime-minus-one sum-product conjecture. For every $a\in\mathbb{N}$ there exist $x,y\in\mathbb{N}$ with $x>y>a$ such that

$$\{x+y,xy\}\subseteq\mathbb{P}-1.$$

This asks for simultaneous additive and multiplicative structure inside the shifted-prime set $\mathbb{P}-1$; the supplied text presents it as an open question and gives no resolution.