# Exploring Prime Number Classification: Achieving High Recall Rate and Rapid Convergence with Sparse Encoding

arXiv: https://arxiv.org/abs/2402.03363 · HTML: https://mlsanity.com/paper/2402.03363/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 15 references that are in the map.
- First posted on arXiv 30 Jan 2024.

## Builds on (most cited first, 4 of 4)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Automatic heterogeneous quantization of deep neural networks for low-latency inference on the edge for particle detectors](https://mlsanity.com/paper/2006.10159/) (2020)
- [Goldbach's Function Approximation Using Deep Learning](https://mlsanity.com/paper/1803.09237/) (2018)

## Built on by (most cited first, 2 of 2)

- [Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective](https://mlsanity.com/paper/2510.21999/) (2025)
- [Testing Transformer Learnability on the Arithmetic Sequence of Rooted Trees](https://mlsanity.com/paper/2512.01870/) (2025)

## Abstract (arXiv)

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 non-prime numbers from an inherently imbalanced sequential series of integers, while exhibiting rapid model convergence before the completion of a single training epoch. We performed training using 106 integers starting from a specified integer and tested on a different range of 2 × 106 integers extending from 106 to 3 × 106, offset by the same starting integer. While constrained by the memory capacity of our resources, which limited our analysis to a span of 3×106, 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.