Machine Learning of the Prime Distribution
This work addresses theoretical connections between machine learning and number theory, but appears incremental as it builds on existing mathematical frameworks.
The authors used maximum entropy methods to derive theorems in probabilistic number theory, including a version of the Hardy-Ramanujan Theorem, and provided a theoretical explanation for experimental observations about the learnability of primes, while arguing that the Erdős-Kac law is unlikely to be discovered by current machine learning techniques.
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 Erdős-Kac law would very unlikely be discovered by current machine learning techniques. Numerical experiments that we perform corroborate our theoretical findings.