17. If $2^{n} \|\left(10^{1002}-4^{501}\right)$, then $n=(\quad)$.
(A) 1002
(B) 1003
(C) 1004
(D) 1005
(E) 1006
17. B.

Notice,
$$
\begin{array}{l} 
10^{1002}-4^{501}=2^{1002} \times 5^{1002}-2^{1002} \\
= 2^{1002} \times (5^{1002}-1) \\
= 2^{1002} \times (5^{501}-1)(5^{501}+1) \\
= 2^{1002} \times (5-1)(5^{500}+5^{499}+\cdots+1) \times \\
(5+1)(5^{500}-5^{499}+5^{498}-5^{497}+\cdots+1) \\
= 2^{1005} \times (5^{500}+5^{499}+\cdots+1) \times \\
3 \times (5^{500}-5^{499}+5^{498}-5^{497}+\cdots+1) .
\end{array}
$$

Thus, \( n=1005 \).