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Cellular Automata (CA) Model for Primality Test

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Cellular Automata (ACRI 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8751))

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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 ′ × S ″, S ′ is the largest factor of S, S ″ = 3,5,7,⋯. The set has at least one CDCA with the state S ′ in its attractor basin; the CA initialized with S ′ reaches the attractor S after S ″ time steps. A number is detected as a prime if no CDCA is synthesized.

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Author information

Authors and Affiliations

  1. Cellular Automata Research Lab (CARL), CARLBio Pvt.Ltd and Alumnus Software Ltd, Saltlake City, Kolkata, 700091, India

    Nirmalya Sundar Maiti, Soumyabrata Ghosh & Parimal Pal Chaudhuri

Authors
  1. Nirmalya Sundar Maiti
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  2. Soumyabrata Ghosh
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  3. Parimal Pal Chaudhuri
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Editor information

Editors and Affiliations

  1. Dept. of Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059, Krakow, Poland

    Jarosław Wąs

  2. Dept. of Electrical and Computer Engineering, Democritus University of Thrace, 67100, Xanthi, Greece

    Georgios Ch. Sirakoulis

  3. CSAI - Complex Systems and Artificial Intelligence Research Center, University of Milano-Bicocca, 20126, Milan, Italy

    Stefania Bandini

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© 2014 Springer International Publishing Switzerland

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Maiti, N.S., Ghosh, S., Chaudhuri, P.P. (2014). Cellular Automata (CA) Model for Primality Test. In: Wąs, J., Sirakoulis, G.C., Bandini, S. (eds) Cellular Automata. ACRI 2014. Lecture Notes in Computer Science, vol 8751. Springer, Cham. https://doi.org/10.1007/978-3-319-11520-7_16

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  • DOI: https://doi.org/10.1007/978-3-319-11520-7_16

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11519-1

  • Online ISBN: 978-3-319-11520-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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