Machine Learning of the Prime Distribution
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910938957873152 |
|---|---|
| author | Kolpakov, Alexander Rocke, Aidan |
| author_facet | Kolpakov, Alexander Rocke, Aidan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12588 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Machine Learning of the Prime Distribution Kolpakov, Alexander Rocke, Aidan Information Theory Artificial Intelligence Machine Learning Number Theory 11N05 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. |
| title | Machine Learning of the Prime Distribution |
| topic | Information Theory Artificial Intelligence Machine Learning Number Theory 11N05 |
| url | https://arxiv.org/abs/2403.12588 |