Infinite Primes From Integer Partitions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913380809310208 |
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| author | Shakov, Anton |
| author_facet | Shakov, Anton |
| contents | Ferrers diagrams are used to visually represent integer partitions. We describe a way to use Ferrers diagrams to uniquely represent integers in terms of their prime factors. This leads to a lower bound on the number of primes less than a given integer, namely $π(x) \geq \frac{\lfloor \lg x \rfloor}{\lg (\lfloor \lg x \rfloor + 1)}$ where $π(x)$ is the prime counting function and $\lg(x)$ denotes the base 2 logarithm. This results in a new proof of the infinitude of primes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03322 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Infinite Primes From Integer Partitions Shakov, Anton General Mathematics 11A51 Ferrers diagrams are used to visually represent integer partitions. We describe a way to use Ferrers diagrams to uniquely represent integers in terms of their prime factors. This leads to a lower bound on the number of primes less than a given integer, namely $π(x) \geq \frac{\lfloor \lg x \rfloor}{\lg (\lfloor \lg x \rfloor + 1)}$ where $π(x)$ is the prime counting function and $\lg(x)$ denotes the base 2 logarithm. This results in a new proof of the infinitude of primes. |
| title | Infinite Primes From Integer Partitions |
| topic | General Mathematics 11A51 |
| url | https://arxiv.org/abs/2311.03322 |