Predictability of consecutive powers 
If $$a^b=c^d+1$$ $$a,b,c,d\in Z$$ $$a,b,c,d>0$$
then $a^b$ and $c^d$ are defined to be "consecutive powers" (atleast in my Q).

Given two large positive integers $a$ and $b$, is it possible to predict, whether approximately or accurately, as to how many "consecutive powers" exist between $a$ and $b$?

By the Catalan conjecture (https://en.wikipedia.org wiki/Catalan's_conjecture ) solved by Mihailescu in 2002, 8 and 9 are the only consecutive powers, so yes, your question can be answered.
