3. The number of positive integers $m$ that make $m^{2}+m+7$ a perfect square is $\qquad$ .
3.2.

It has been verified that when $m=1$, $m^{2}+m+7=9$ is a perfect square;

when $m=2,3,4,5$, $m^{2}+m+7$ are not perfect squares;

when $m=6$, $m^{2}+m+7=49$ is a perfect square.

When $m>6$, $m^{2}+m+7$ are not perfect squares.
Therefore, there are only 2 positive integers $m$ that meet the condition.