2017/02/26 by Sathwik Karnik, Karnik, Sathwik
Computer Science · Mathematics · #Analytic Number Theory Research #Chaos-based Image/Signal Encryption #Computability, Logic, AI Algorithms #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1702.08066
openalex publication_date 2017/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.