4. Group all positive integers that are coprime with 2012 in ascending order, with the $n$-th group containing $2n-1$ numbers:
$$
\{1\},\{3,5,7\},\{9,11,13,15,17\}, \cdots \text {. }
$$

Then 2013 is in the $\qquad$ group.
4.32.

Notice that, $2012=2^{2} \times 503$, where $2$ and $503$ are both prime numbers.

Among the positive integers not greater than 2012, there are 1006 multiples of 2, 4 multiples of 503, and 2 multiples of $2 \times 503$. Therefore, the numbers that are not coprime with 2012 are
$$
1006+4-2=1008 \text { (numbers). }
$$

Thus, among the positive integers not greater than 2012, the numbers that are coprime with 2012 are
$$
2012-1008=1004 \text { (numbers). }
$$

Hence, 2013 is in the 1005th position.
Also, $31^{2}<1005<32^{2}$, that is
$$
\begin{array}{l}
1+3+\cdots+(2 \times 31-1)<1005 \\
<1+3+\cdots+(2 \times 32-1) .
\end{array}
$$

Thus, 2013 is in the 32nd group.