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.

该研究论文介绍了一种机器学习和数论相交的新方法，关注的是素数和非素数的分类。研究的核心是开发了一种高度稀疏的编码方法，与传统的神经网络结构相结合。这种组合已经显示出有希望的结果，在识别自然存在不平衡的整数序列中的素数方面，召回率达到99％以上，对于非素数为79％，而且在完整的单次训练迭代前就展现出快速的模型收敛。我们进行了$10^6$个整数的训练，从指定的整数开始，并在从$10^6$到$3 	imes 10^6$的不同范围的$2 	imes 10^6$个整数上进行测试，其起始整数相同。虽然受到我们资源的内存容量的限制，将分析限制在$3 	imes 10^6$的范围内，但我们认为这项研究对机器学习在素数分析中的应用做出了贡献。这项工作旨在展示这种应用的潜力，并希望在不同领域中激发进一步的探索和可能性。

探索质数分类：以稀疏编码实现高召回率和快速收敛