探索素数分类：通过稀疏编码实现高召回率和快速收敛
Exploring Prime Number Classification: Achieving High Recall Rate and Rapid Convergence with Sparse Encoding
AI总结：
本文提出一种结合机器学习与数论的新方法，通过稀疏编码与传统神经网络结合，实现高召回率和快速收敛，验证了在素数识别中的有效性。
摘要：
本文提出了一种在机器学习和数论交汇处的新方法，专注于素数和非素数的分类。我们的研究核心是开发了一种高度稀疏的编码方法，并与传统神经网络架构相结合。这种方法在识别素数时达到了超过99%的召回率，在识别非素数时达到了79%的准确率，同时在单个训练周期内表现出快速的模型收敛。我们使用10^6个整数进行训练，从指定整数开始，并在10^6到3×10^6的范围内测试了2×10^6个整数，偏移量相同。尽管受限于资源的内存容量，使我们的分析范围仅限于3×10^6，但我们相信我们的研究为机器学习在素数分析中的应用做出了贡献。本文旨在展示此类应用的潜力，并希望激发在不同领域中的进一步探索和可能性。
英文摘要：
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 $10^6$ integers starting from a specified integer and tested on a different range of $2 \times 10^6$ integers extending from $10^6$ to $3 \times 10^6$, offset by the same starting integer. While constrained by the memory capacity of our resources, which limited our analysis to a span of $3\times10^6$, 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
