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arXiv · 1512.00444

Infinitely Many Carmichael Numbers for a Modified Miller-Rabin Prime Test

Eric Bach·Rex Fernando
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Abstract

We define a variant of the Miller-Rabin primality test, which is in between Miller-Rabin and Fermat in terms of strength. We show that this test has infinitely many "Carmichael" numbers. We show that the test can also be thought of as a variant of the Solovay-Strassen test. We explore the growth of the test's "Carmichael" numbers, giving some empirical results and a discussion of one particularly strong pattern which appears in the results.

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Eric Bach, Rex Fernando. 2015-12-02. Infinitely Many Carmichael Numbers for a Modified Miller-Rabin Prime Test. https://arxiv.org/abs/1512.00444

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