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arXiv · 1702.08066

On the Classification and Algorithmic Analysis of Carmichael Numbers

Sathwik Karnik
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Abstract

In this paper, we study the properties of Carmichael numbers, false positives to several primality tests. We provide a classification for Carmichael numbers with a proportion of Fermat witnesses of less than 50%, based on if the smallest prime factor is greater than a determined lower bound. In addition, we conduct a Monte Carlo simulation as part of a probabilistic algorithm to detect if a given composite number is Carmichael. We modify this highly accurate algorithm with a deterministic primality test to create a novel, more efficient algorithm that differentiates between Carmichael numbers and prime numbers.

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Sathwik Karnik. 2017-02-26. On the Classification and Algorithmic Analysis of Carmichael Numbers. https://arxiv.org/abs/1702.08066

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