3. Find a prime number $p$ greater than 2, such that the parabola
$$
y=\left(x-\frac{1}{p}\right)\left(x-\frac{p}{2}\right)
$$

has a point $\left(x_{0}, y_{0}\right)$ where $x_{0}$ is a positive integer and $y_{0}$ is the square of a prime number.