$19422 *$ Find the largest integer $x$ that makes $4^{27}+4^{1000}+4^{x}$ a perfect square.
Parse $4^{27}+4^{1000}+4^{x}=2^{54}\left(1+2 \cdot 2^{1945}+2^{2 x-54}\right)$, when $2 x-54=2 \times 1945$, i.e., $x=1972$, it is a perfect square.

When $x>1972$, $2^{2(x-27)}<1+2 \cdot 2^{1945}+2^{2(x-27)}<\left(2^{x-27}+1\right)^{2}$. That is, $1+2 \cdot$ $2^{1945}+2^{2 x-54}$ lies between the squares of two consecutive natural numbers, so it cannot be a perfect square.
Therefore, the maximum integer $x$ sought is 1972.