This chapter returns to the question of deciding whether a given odd number m is prime. The a-pseudoprime test of Chapter 10B will not work on Carmichael numbers. We first describe an idea of Alford that shows that there are many Carmichael numbers. Then we develop the strong a-pseudoprime test and prove that every composite number m fails the strong a-pseudoprime test for at least half of the numbers a < m. Thus there are no composite numbers that are “strong Carmichael numbers”.
KeywordsPrime Divisor Chinese Remainder Theorem Fermat Number Composite Number Generalize Riemann Hypothesis
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