The loop equation conjecture for every element of S

Let $S$ be the set of odd primes, and for $a,b\in S$ let $a\bullet b$ denote the smallest prime strictly greater than $|a-b|$. Loop equation conjecture. For every $x\in S$, the equation

$$a\bullet b=x$$

has infinitely many solutions $(a,b)\in S^2$. This is presented as an analogue of Polignac's conjecture and is stated to be equivalent to it; the source also explains that the twin prime conjecture corresponds to the case $x=3$.