# Greatest prime factor of n and n+1

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 $$p,q>100$$?