  Let $C(a ),C(b)\subset \lbrack 0,1]$ be the central Cantor sets generated by
sequences $ a,b \in (0,1)^{\mathbb{N}}$. The first main result of the paper
gives a necessary and a sufficient condition for sequences $a$ and $b$ which
inform when $C(a )-C(b)$ is equal to $[-1,1]$ or is a finite union of closed
intervals. One of the corollaries following from this results shows that the
product of thicknesses of two central Cantor sets which algebraic difference is
an interval may be arbitrarily small. We also show that there are sets $C(a)$
and $C(b)$ with the Hausdorff dimension equal to $0$ such that their algebraic
difference is an interval. Finally, we give a full characterization of the
case, when $C(a )-C(b)$ is equal to $[-1,1]$ or is a finite union of closed
intervals.
