• Lindsay N. Childs
Part of the Undergraduate Texts in Mathematics book series (UTM)


This chapter returns to the question of deciding whether a given odd number m is prime. The a-pseudoprime test of Chapter 10D will not work on Carmichael numbers. We first describe a recent idea of Alford which shows that there are many Carmichael numbers. Then we develop the strong a-pseudoprime test and present a theorem of Rabin that every composite number m fails the strong a-pseudoprime test for most a < m. We conclude this chapter with a proof of a weak version of Rabin’s theorem; the next chapter gives a proof of the strong version of Rabin’s theorem.


Chinese Remainder Theorem Congruence Class Composite Number Generalize Riemann Hypothesis Primitive Root Modulo 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Lindsay N. Childs
    • 1
  1. 1.Department of MathematicsSUNY at AlbanyAlbanyUSA

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