+ An $n-$domino is a connected shape consisting of $n$ unit squares, for example, Figure 1 is an 8-domino.

A dinosaur refers to a domino made up of at least 2007 unit squares. A dinosaur is called prime if it cannot be divided into two or more dinosaurs. Question: What is the maximum number of unit squares a prime dinosaur can have?
Let $s=2007$, the answer is $4(s-1)+1$.
First, we construct a prime dinosaur consisting of $4(s-1)+1$ unit squares. As shown in Figure 2, it is a "cross" shape, consisting of a central square and four "arms" of length $s-1$ squares each. It is easy to see that it is a prime dinosaur.
Next, we prove that there is no prime dinosaur with more than $4(s-1)+1$ squares.
Let $D$ be a dinosaur with no fewer than $4(s-1)+2$ squares, and divide it into two dominoes, one $R$ and one $B$, such that $R \cap B=\varnothing, R \cup B=D$. Suppose $|R| \leqslant s-1$, then $R$ can be expanded to a domino $\tilde{R} \supset R$, and let $\tilde{B}=D \backslash \tilde{R}$, such that at least one of the following conditions holds:
(1) $|\tilde{R}| \geqslant s$ and $|\tilde{B}| \geqslant s$;
(2) $|\tilde{R}|=|R|+1$;
(3) $|R|<s-1$,
$$
\left|C_{3}\right| \geqslant s \text{. }
$$

Let $\tilde{B}=C_{3}$, then
$$
|\tilde{R}|=|R|+\left|C_{1}\right|+\left|C_{2}\right|+1
$$

If $|\tilde{B}| \leqslant 3 s-2$, then $|\tilde{R}| \geqslant s$, so (1) holds.
If $|\tilde{B}| \geqslant 3 s-1$, then $|\tilde{R}| \leqslant s-1$, and $|\tilde{R}|>|R|$, so (3) holds.

Therefore, starting from the beginning, first divide $D$ into two dominoes $R$ and $B$, without loss of generality, assume $|R|=1$, then repeatedly use the above conclusion, since whether (2) or (3), $|R|$ is strictly increasing and always no more than $s$, so there must be a moment when (1) occurs, thus $D$ is not a prime dinosaur.

In summary, a prime dinosaur has at most $4(s-1)+1=8025$ small squares.