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 Y.-H. 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：在本工作中，我们利用最大熵方法推导出概率数论中的若干定理，包括哈代-拉马努金定理的一个版本。同时，我们提供理论论证以解释何宜华关于质数可学习性的实验观察，并提出厄多斯-卡克定律极不可能被当前机器学习技术发现的观点。我们所进行的数值实验印证了上述理论结果。