Cellular Automata (CA) Model for primality test

Abstract

Theory and application of Cellular automata (CA) as a global Transform for detecting compositeness of a number is reported. To test an n bit odd valued number N in the range 2n−1 to (2n-1), a Compositeness Detecting CA (CDCA) set is designed with N = S as a Self Loop Attractor (SLA) State, where S = S ʹ × S ʺ , S ʹ is the largest factor of S, S ʺ = 3,5,7,…. The set has at least one CDCA with the state Sʹ in its attractor basin; the CA initialized with Sʹ reaches the attractor S after S ʺ time steps. A number is detected as a prime if no CDCA is synthesized.