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Deterministic and Las Vegas primality testing algorithms

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Automata, Languages and Programming (ICALP 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 194))

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Abstract

Some deterministic and Las Vegas primality tests are presented. Under certain conditions, they run in polynomial time. In particular, there is a polynomial time Las Vegas algorithm deciding primality of n, when n hat at most 2 prime factors and n \(\mathop \mp \limits^ + \)1 mod 24.

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References

  1. L.M. Adleman, C. Pomerance and R.S. Rumely, On distinguishing Prime Numbers from Composite Numbers. Annals of Math. 117 (1983), 173–206.

    Google Scholar 

  2. N.C. Ankeny, The Least Quadratic Non-Residue. Annals of Math. 55 (1952), 65–72.

    Google Scholar 

  3. E. Bach, Fast Algorithms under the Extended Riemann Hypothesis: A Concrete Estimate. 14th STOC (1982), 290–295.

    Google Scholar 

  4. N.G. de Bruijn, On the Number of Positive Integers ≤ x and Free of Prime Factors > y, II. Proc. Koninklijke Nederlandse Akademie van Wettenschappen. Ser. A 69 (=Indag.Math.28) (1966), 239–247.

    Google Scholar 

  5. H. Cohn, Advanced Number Theory. Dover, New York, 1980.

    Google Scholar 

  6. G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers. Oxford University Press, Oxford, 1979.

    Google Scholar 

  7. D.E. Knuth, The Art of Computer Programming, Vol. 2: Seminumerical Algorithms. Addison-Wesley, Reading, 1981.

    Google Scholar 

  8. S. Lang, Algebra. Addison-Wesley, Reading, 1984.

    Google Scholar 

  9. D.H. Lehmer, An Extended Theory of Lucas'Functions. Annals of Math. 31 (1930), 419–448.

    Google Scholar 

  10. E. Lucas, Théorie des fonctions numériques simplement périodiques. Amer. J. Math 1 (1878), 184–239, 289–321.

    MathSciNet  Google Scholar 

  11. G.L. Miller, Riemann's Hypothesis and Tests for Primality. J. of Computer and System Sciences 13 (1976), 300–317.

    Google Scholar 

  12. K.K. Norton, Numbers with Small Prime Factors, and the Least k-th Power Non-Residue. Memoirs of the AMS No. 106, 1971.

    Google Scholar 

  13. J. Oesterlé, Versions effectives du théorème de Chebotarew sous l'hypothèse de Riemann généralisée, Journées Arithmétiques de Luminy, Astérisque 61 (1979), 165–167.

    Google Scholar 

  14. D.A. Plaisted, Fast Verification, Testing and Generation of Large Primes. Theoretical Computer Science 9 (1979), 1–16.

    Article  Google Scholar 

  15. K. Prachar, Primzahlverteilung. Springer, Berlin, 1957.

    Google Scholar 

  16. M.O. Rabin, Probabilistic Algorithm for Testing Primality. J. of Number Theory 12 (1980), 128–138.

    Article  Google Scholar 

  17. C.L. Siegel, Ueber die Classenzahl quadratischer Zahlkörper. Acta Arithm. 1 (1935), 83–86.

    Google Scholar 

  18. R. Solovay and V. Strassen, A Fast Monte-Carlo Test for Primality. SIAM J. on Computing 6 (1977), 84–85.

    Article  Google Scholar 

  19. I.N. Stewart and D.O. Tall, Algebraic Number Theory. Chapman and Hall, London, 1979.

    Google Scholar 

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Authors and Affiliations

  1. Institut für Angewandte Mathematik der Universität Zürich, CH-8001, Zürich

    Martin Fürer

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  1. Martin Fürer
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Wilfried Brauer

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© 1985 Springer-Verlag Berlin Heidelberg

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Fürer, M. (1985). Deterministic and Las Vegas primality testing algorithms. In: Brauer, W. (eds) Automata, Languages and Programming. ICALP 1985. Lecture Notes in Computer Science, vol 194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015745

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  • DOI: https://doi.org/10.1007/BFb0015745

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15650-5

  • Online ISBN: 978-3-540-39557-7

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