On the Density of Prime Imbalances in the Unit Interval
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916793820381184 |
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| author | Bilokon, Paul Alexander |
| author_facet | Bilokon, Paul Alexander |
| contents | We prove that the set of normalized differences between primes, defined as $S = \{(p-q)/(p+q) : p > q \text{ are primes}\}$, is dense in the open unit interval $(0,1)$. Our proof provides an explicit construction algorithm with quantitative bounds, relying on elementary results from prime number theory including Bertrand's postulate and explicit bounds on prime gaps in long intervals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12063 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Density of Prime Imbalances in the Unit Interval Bilokon, Paul Alexander General Mathematics We prove that the set of normalized differences between primes, defined as $S = \{(p-q)/(p+q) : p > q \text{ are primes}\}$, is dense in the open unit interval $(0,1)$. Our proof provides an explicit construction algorithm with quantitative bounds, relying on elementary results from prime number theory including Bertrand's postulate and explicit bounds on prime gaps in long intervals. |
| title | On the Density of Prime Imbalances in the Unit Interval |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2506.12063 |