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

2015/12/01 by Eric Bach, Bach, Eric, Rex Fernando +1
Computer Science · Mathematics · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT) #cs.DS #math.NT

paper · pdf · doi:10.48550/arxiv.1512.00444

17 pages (21 with appendix)

openalex publication_date 2015/12/01 · arxiv created 2015/12/02 · arxiv updated 2015/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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