Abstract: In this paper we study the dynamics for the prime principle. The p-nonlinear equations are derived from the prime principle. It defines the p-chaotic functions and studies the local solutions and global stability for the p-nonlinear equations. It suggests a new method for studying the nonlinear equations that studying the stability and instability of the p-nonlinear equations is transformed into studying the stability and instability for the nonliner terms of de^A/dt in the chaotic equations.