3. If a positive integer can be expressed as the difference of squares of two consecutive even numbers, it is called a "mysterious number" (for example, 4 $=2^{2}-0^{2}, 12=4^{2}-2^{2}, 20=6^{2}-4^{2}$). Which of the following statements about mysterious numbers is correct? ( ).
(1) 2008 is a mysterious number;
(2) The difference of squares of any two positive odd numbers is a mysterious number;
(3) The difference of squares of any two positive odd numbers is not a mysterious number;
(4) Among the 100 numbers from 1 to 100, there are 13 mysterious numbers.
(A) 1
(B) 2
(C) 3
(D) 4
3. B.

Let two consecutive even numbers be $2k+2$ and $2k$, then
$$
(2k+2)^2 - (2k)^2 = 4(2k+1).
$$

Since $2k+1$ is an odd number, the mysterious number is a multiple of 4 but not a multiple of 8.
Let any two positive odd numbers be $2m+1$ and $2n+1$, then $(2m+1)^2 - (2n+1)^2 = 4(m+n+1)(m-n)$.
Since $m+n+1$ and $m-n$ have opposite parity, $(2m+1)^2 - (2n+1)^2$ is a multiple of 8. Therefore, $(2m+1)^2 - (2n+1)^2$ is not a mysterious number.
Since $2008 = 8 \times 251$, 2008 is not a mysterious number.
It is not difficult to verify that the mysterious numbers between $1 \sim 100$ are $4 \times 1, 4 \times 3, \cdots, 4 \times 25$. There are a total of 13 such numbers.
In summary, (3) and (4) are correct.