4. If a positive integer can be expressed as the difference of squares of two consecutive even numbers, it is called a "Morning Star Number" (such as $4=2^{2}-0^{2}, 12=4^{2}-2^{2}, 20=6^{2}-4^{2}$). Among the following statements about Morning Star Numbers, the correct ones are ( ) in number.
(1) 2010 is a Morning Star Number;
(2) The difference of squares of any two positive odd numbers is a Morning Star Number;
(3) The difference of squares of any two positive odd numbers is not a Morning Star Number;
(4) Among the numbers 1 to 100, there are 13 Morning Star Numbers.
(A) 1
(B) 2
(C) 3
(D) 4
4. B.

Let two consecutive even numbers be $2 k+2$ and $2 k$. Then $(2 k+2)^{2}-(2 k)^{2}=4(2 k+1)$.
Therefore, Chen Yao numbers are multiples of 4, but not multiples of 8. Let any two positive odd numbers be $2 m+1, 2 n+1$. Then
$$
\begin{array}{l}
(2 m+1)^{2}-(2 n+1)^{2} \\
=4[m(m+1)-n(n+1)] .
\end{array}
$$

Thus, 8 divides $\left[(2 m+1)^{2}-(2 n+1)^{2}\right]$.
Therefore, statement (2) is incorrect, and statement (3) is correct.
Also, $4 \times 2010$, so statement (1) is incorrect.
It is not difficult to verify: Chen Yao numbers between 1 and 100 are $4 \times 1, 4 \times 3, \cdots, 4 \times 25$. There are a total of 13.
Thus, statement (4) is correct.