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Primality testing algorithms [after Adleman, Rumely and Williams]

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Séminaire Bourbaki vol. 1980/81 Exposés 561–578

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 901))

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References

  1. L.M. ADLEMAN, On distinguishing prime numbers from composite numbers (abstract), Proc. 21st Annual IEEE Symposium on Foundations of Computer Science (1980), 387–406.

    Google Scholar 

  2. L.M. ADLEMAN, C. POMERANCE, R.S. RUMELY, On distinguishing prime numbers from composite numbers, preprint.

    Google Scholar 

  3. S.U. CHASE, D.K. HARRISON, A. ROSENBERG, Galois theory and Galois cohomology of commutative rings, Memoirs Amer. Math. Soc. 52 (1965), 15–33.

    MATH  MathSciNet  Google Scholar 

  4. F. DEMEYER, E. INGRAHAM, Separable algebras over commutative rings, Lecture Notes in Mathematics 181, Springer, Berlin 1971.

    MATH  Google Scholar 

  5. R.K. GUY, How to factor a number, Proc. Fifth Manitoba Conf. Numer. Math., Utilitas, Winnipeg (1975), 49–89.

    Google Scholar 

  6. D.E.KNUTH, The art of computer programming, vol. 2, Seminumerical algorithms, second edition, Addison-Wesley, Reading 1981.

    MATH  Google Scholar 

  7. S. LANG, Cyclotomic fields, Springer, Berlin 1978.

    MATH  Google Scholar 

  8. H.W. LENSTRA, Jr., Euclid's algorithm in cyclotomic fields, J. London Math. Soc. (2) 10 (1975), 457–465.

    MATH  MathSciNet  Google Scholar 

  9. J.M. POLLARD, Theorems on factorization and primality testing, Proc. Cambridge Philos. Soc. 76 (1974), 521–528.

    Article  MATH  MathSciNet  Google Scholar 

  10. K. PRACHAR, Über die Anzahl der Teiler einer natürlichen Zahl, welche die Form p-1 haben, Monatsh. Math. 59 (1955), 91–97.

    Article  MATH  MathSciNet  Google Scholar 

  11. C.P. SCHNORR, Refined analysis and improvements on some factoring algorithms, to appear in: Automata, Languages and Programming, Eighth Colloquium, Haifa 1981, Lecture Notes in Computer Science, to appear.

    Google Scholar 

  12. R. SOLOVAY, V. STRASSEN, A fast Monte-Carlo test for primality, SIAM J. Comput. 6 (1977), 84–85; erratum, 7 (1978), 118.

    Article  MATH  MathSciNet  Google Scholar 

  13. H.C. WILLIAMS, Primality testing on a computer, Ars Combin. 5 (1978), 127–185.

    MATH  MathSciNet  Google Scholar 

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© 1981 N. Bourbaki

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Lenstra, H.W. (1981). Primality testing algorithms [after Adleman, Rumely and Williams]. In: Séminaire Bourbaki vol. 1980/81 Exposés 561–578. Lecture Notes in Mathematics, vol 901. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0097201

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  • DOI: https://doi.org/10.1007/BFb0097201

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11176-4

  • Online ISBN: 978-3-540-38956-9

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