166 In the range from 1 to 1000, there are $\qquad$ positive integers $n$ such that $n^{1993}+1$ and $n^{1994}+1$ are coprime.
166 500. Generally, we have $\left(n^{m+1}+1, n^{m}+1\right)=\left(\left(n^{m}+1\right) \cdot n-n+1, n^{m}+1\right)=$ $\left(n^{m}+1, n-1\right)=\left((n-1) \cdot n^{n-1}+n^{m-1}+1, n-1\right)=\left(n^{n-1}+1, n-1\right)$ $=\cdots=(n+1, n-1)=(2, n-1)=\left\{\begin{array}{l}2, \text { when } n \text { is odd; } \\ 1, \text { when } n \text { is even. }\end{array}\right.$ (Here $(a, b)$ denotes the greatest common divisor of $a$ and $b$.) Since there are 500 even numbers between $1 \sim 1000$, there are 500 positive integers $n$ such that $n^{1993}+1$ and $n^{1994}+1$ are coprime.