Certainly $b\pm a$ have no particularly small factors. It would be interesting to know what results you have for moderate size $x.$
It is probably no help to you, but I am reminded of the quirky paper Primes at a Glance. In case $ab$ is the product of all primes up to $p$ and $1 \lt b-a \lt p^2$ (or I guess even the product of the next two primes) then $b-a$ is clearly prime. That paper shows that such an occurrence is rare and discusses related matters.