Abstract: Resolver is an important angle test instrument in many automatic control systems. Currently, concentric sinusoidal winding combination is recommended in various literatures as the guideline to single pole wound resolver design. Certain products and patent applications have already appeared in recent years by prime number winding combination, but corresponding theoretic analysis in such design is still difficult to be found. Based on the theory of magnetic harmonics, this paper derived the slot ripple error limit and put forward the mathematical basis to achieve high precision magnetic field by skewed prime number winding combination. There's no theoretical zero position error in the prime number winding combinations, and the orthogonal position error is no more than their function error. Numeric analysis and FEM simulation were carried out, and the distribution of magnetic field error was demonstrated with respect to different winding combinations. An appropriate selection method was clarified to select skewed prime number winding combination. It is proved that the recommended selection method in prime number skewed winding combination is right and effective by the development and test of a (7:10) prototype resolver with the help of magnetic potential harmonics and the function error analysis.