Imbalance Prime Sieving: Every Prime Gap Is a Result of a Möbius Imbalance Obstruction
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915405479542784 |
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| author | Bilokon, Paul Alexander |
| author_facet | Bilokon, Paul Alexander |
| contents | We introduce a novel sieve for prime numbers based on detecting topological obstructions in a Möbius-transformed rational metric space. Unlike traditional sieves which rely on divisibility, our method identifies primes as those numbers which contribute new, non-colliding imbalance conjugates. This provides both an exact algorithm for prime enumeration and a new geometric interpretation of prime gaps. This sieve constructs a topological obstruction theory over rational pairs (p, q), from which we observe that every prime gap is a consequence of a collision in this transformed imbalance space. Our empirical results demonstrate that this method precisely filters the prime numbers up to a specified bound, with potential implications for new number-theoretic models and sieving algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_16821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Imbalance Prime Sieving: Every Prime Gap Is a Result of a Möbius Imbalance Obstruction Bilokon, Paul Alexander General Mathematics 11N36, 11N05 F.2.1 We introduce a novel sieve for prime numbers based on detecting topological obstructions in a Möbius-transformed rational metric space. Unlike traditional sieves which rely on divisibility, our method identifies primes as those numbers which contribute new, non-colliding imbalance conjugates. This provides both an exact algorithm for prime enumeration and a new geometric interpretation of prime gaps. This sieve constructs a topological obstruction theory over rational pairs (p, q), from which we observe that every prime gap is a consequence of a collision in this transformed imbalance space. Our empirical results demonstrate that this method precisely filters the prime numbers up to a specified bound, with potential implications for new number-theoretic models and sieving algorithms. |
| title | Imbalance Prime Sieving: Every Prime Gap Is a Result of a Möbius Imbalance Obstruction |
| topic | General Mathematics 11N36, 11N05 F.2.1 |
| url | https://arxiv.org/abs/2507.16821 |