13. Ordered pairs of positive integers $(a, b)(a<b)$ satisfy $a+b=2008$, and $a, b$ are coprime. Then the number of pairs $(a, b)$ that satisfy the condition is $\qquad$.
13.500.

Since $2008=2^{3} \times 251$, therefore, $a$ cannot be an even number, and it cannot be a multiple of 251. And $a \leqslant 1003$, so the number of $a$ is $1003-501-2=500$.