AMC 12 2004a Problem 16

The set of all real numbers $x$ for which

$$\log_{2004}(\log_{2003}(\log_{2002}(\log_{2001}{x})))$$

is defined is $\{x\mid x > c\}$. What is the value of $c$?

$\textbf {(A) } 0 \textbf {(B) }2001^{2002} \textbf {(C) }2002^{2003} \textbf {(D) }2003^{2004} \textbf {(E) }2001^{2002^{2003}}$