Real-Time Generation of Primes by a 1-Bit-Communication Cellular Automaton

Abstract

It is shown that an infinite prime sequence can be generated in real-time by a cellular automaton having 1-bit inter-cell communications (CA_{1-bit}). The algorithm presented is based on the classical sieve of Eratosthenes, and its implementation will be made on a CA_{1-bit} using 34 internal states and 71 transition rules.