The circle P in this question is a moving circle, which can be analyzed from a special position (tangency) and divided into right tangency and left tangency, and then solved. If a circle is tangent to a straight line, the distance from the center of the circle to the straight line should be equal to the radius of the circle 1, which is obtained from the functional relationship of the straight line.

A (-3,0), B(0, root number 3), then the angle BAO = 30, so when tangent, AP=2, and point P may be on the left or right side of point A, so to intersect, it should be between these two situations, that is, the abscissa of point P should be between-1 and -5. At this time, there are three points p, and the abscissa is an integer (-2,0) (-3,0) (-4,0).

Note: The intersection of a straight line and a circle does not include two tangents.