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Infinitely Many Carmichael Numbers for a Modified Miller-Rabin Prime Test
December 01, 2015 · Declared Dead · 🏛 International Symposium on Symbolic and Algebraic Computation
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Authors
Eric Bach, Rex Fernando
arXiv ID
1512.00444
Category
math.NT
Cross-listed
cs.DS
Citations
1
Venue
International Symposium on Symbolic and Algebraic Computation
Last Checked
1 month ago
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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