For a positive integer $ n$ we denote its largest prime factor by $ \operatorname{gpf}(n)$ . Let’s call a pair of distinct primes $ (p,q)$ $ \textbf{nice}$ if there are no natural numbers $ n$ such that $ \operatorname{gpf}(n)=p, \operatorname{gpf}(n+1)=q$ or $ \operatorname{gpf}(n)=q, \operatorname{gpf}(n+1)=p$ . For example, $ (2,19)$ is nice.

Are there nice pairs $ (p,q)$ with $ p,q>100$ ?