Classification Accuracy by Deviation-based Classification Method with the Number of Training Documents

Abstract

This paper presents a novel approach at the intersection of machine learning and number theory, focusing on the classification of prime and non-prime numbers. At the core of our research is the development of a highly sparse encoding method, integrated with conventional neural network architectures. This combination has shown promising results, achieving a recall of over 99% in identifying prime numbers and 79% for nonprime numbers from an inherently imbalanced sequential series of integers, while exhibiting rapid model convergence before the completion of a single training epoch. An interesting aspect of our findings includes the analysis of false positives, where we found a consistent misclassification of certain non-prime numbers, particularly semi-primes. We performed training using 10 6 integers starting from a specified integer and tested on a different range of 2 × 10 6 integers extending from 10 6 to 3 × 10 6 , offset by the same starting integer. While constrained by the memory capacity of our resources, which limited our analysis to a span of 3 × 10 6 , we believe that our study contribute to the application of machine learning in prime number analysis. This work aims to demonstrate the potential of such applications and hopes to inspire further exploration and possibilities in diverse fields.