4. 64 .

If three numbers are taken out and are not adjacent, denoted as $a_{1}, a_{2}, a_{3}$, then they satisfy
$$
3 \leqslant a_{1}+2<a_{2}+1<a_{3} \leqslant 10,
$$

This is equivalent to selecting three numbers from $\{3,4, \cdots, 10\}$, thus, the number of ways that meet the requirement is $\mathrm{C}_{10}^{3}-\mathrm{C}_{8}^{3}=64$.
4. Choose three different numbers from $\{1,2, \cdots, 10\}$, such that at least two of them are consecutive, there are $\qquad$ ways to do this.