［Solution］（1）Let $x$ be the base. If $x>2$, then we have
$$\begin{aligned} 10201 & =x^{4}+2 x^{2}+1 \\ & =\left(x^{2}+1\right)^{2} . \end{aligned}$$

It is clearly a composite number.
$$\text { (2) } \begin{aligned} \text { Since } 10101 & =x^{4}+x^{2}+1 \\ & =\left(x^{2}+x+1\right)\left(x^{2}-x+1\right) . \end{aligned}$$

And both factors on the right side of the equation are greater than 1, so the product is a composite number.