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Real-time generation of primes by a one-dimensional cellular automaton with 11 states

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Mathematical Foundations of Computer Science 1997 (MFCS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1295))

Abstract

A 11-state one-dimensional cellular automaton is constructed which generates the primes in the following sense: The content of the 0-th cell at time t is equal to ‘1’ if t is a prime, and is equal to ‘0’ otherwise. The neighbourhood type of this CA is (-1, 0, 1), i.e. the most usual one. At time t = 0 only the 0-th cell is in the non-quiescent state (here ‘0’ is not the quiescent state). Further, a one-dimensional CA is constructed with the radius 12 but with two states only which also generates the primes. (At time t - 0 only the 1-st cell is in non-quiescent state.) Also a generalized Pascal triangle with 83 distinct elements is constructed which generates the odd primes in a similar sense. Hence the primes can be real-time generated also by a 83-state one-dimensional CA with the neighborhood type (-1,1).

This research was partially supported by GA ČR No 201/95/0976 “HypercompleX” and by Grant 2/4O34/97 of VEGA (SAV)

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References

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 81473, Bratislava, Slovakia

    Ivan Korec

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  1. Ivan Korec
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Igor Prívara Peter Ružička

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© 1997 Springer-Verlag Berlin Heidelberg

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Korec, I. (1997). Real-time generation of primes by a one-dimensional cellular automaton with 11 states. In: Prívara, I., Ružička, P. (eds) Mathematical Foundations of Computer Science 1997. MFCS 1997. Lecture Notes in Computer Science, vol 1295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029979

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  • DOI: https://doi.org/10.1007/BFb0029979

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63437-9

  • Online ISBN: 978-3-540-69547-9

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