In the present work we use maximum entropy methods to derive several theorems in probabilistic number theory, including a version of the Hardy-Ramanujan Theorem. We also provide a theoretical argument explaining the experimental observations of Yang-Hui He about the learnability of primes, and posit that the Erd\H{o}s-Kac law would very unlikely be discovered by current machine learning techniques. Numerical experiments that we perform corroborate our theoretical findings.

翻译：本研究采用最大熵方法推导了概率数论中的若干定理，包括哈代-拉马努金定理的一个变体。针对杨辉关于素数可学习性的实验观测，我们提出了理论论证予以解释，并指出埃尔德什-卡茨定律极不可能被现有机器学习技术所发现。我们进行的数值实验证实了这些理论发现。