Real-time generation of primes by a 1-bit-communication cellular automaton

Authors:
Hiroshi Umeo;Naoki Kamikawa
Affiliations:
Faculty of Information Science and Technology, Osaka Electro-Communication University, Neyagawa-shi, Hatsu-cho, 18-8, Osaka, Japan;Noritsu Koki Co., Ltd., Wakayama-shi, Umehara, 579-1, Wakayama, 640-8550, Japan
Venue:
Fundamenta Informaticae - Special issue on cellular automata
Year:
2003

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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 (CA1-bit). The algorithm presented is based on the classical sieve of Eratosthenes, and its implementation will be made on a CA1-bit using 34 internal states and 71 transition rules.