Here’s an example of using 400 segments. Note that you can just keep the threads in one group and the head in another group. The slicer will figure it out.
There are many ways to make screw threads in SketchUp. Here is one more using the Spirix plugin …
One of the aspects of SketchUp that makes circular objects such an issue in 3D printing is the use of line segments to approximate an arc. This is glossed over by the visual smoothing functions that make even relatively crude circles look smooth. While this is fine for visual aids and drawings, any circular arcs that will be 3D printed will need many more line segments than usual. However, this is …