How Prime Factors Form Fractals
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866929725964812288 |
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| author | Tillman, Micah D. |
| author_facet | Tillman, Micah D. |
| contents | We explore a new sieve that generates both primes and prime factorizations, without resorting to division. We demonstrate that the integer sequences generated by the sieve are the p-adic valuations of n, and that each is a fractal sequence. We then show that these sequences produce geometrical fractals like the Levy Dragon. We end by showing the connection between the odd part of n integer sequence and the Heighway Dragon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15743 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How Prime Factors Form Fractals Tillman, Micah D. General Mathematics 28A80 (Primary), 11A41 (Primary), 11A51 (Secondary), 11E95 (Secondary), 11N35 Sieves (Secondary), 11Y55 (Secondary), 68W32 (Secondary) We explore a new sieve that generates both primes and prime factorizations, without resorting to division. We demonstrate that the integer sequences generated by the sieve are the p-adic valuations of n, and that each is a fractal sequence. We then show that these sequences produce geometrical fractals like the Levy Dragon. We end by showing the connection between the odd part of n integer sequence and the Heighway Dragon. |
| title | How Prime Factors Form Fractals |
| topic | General Mathematics 28A80 (Primary), 11A41 (Primary), 11A51 (Secondary), 11E95 (Secondary), 11N35 Sieves (Secondary), 11Y55 (Secondary), 68W32 (Secondary) |
| url | https://arxiv.org/abs/2502.15743 |