{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/imbalance-prime-sieving-every-prime-gap-is-a","title":"Imbalance Prime Sieving: Every Prime Gap Is a Result of a Möbius Imbalance Obstruction","arxiv_id":null,"date":"2025-07-01","proceeding":"SSRN 2025 7","authors":["Paul Alexander Bilokon"],"abstract":"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.","url_abs":"https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5334569","url_pdf":"https://papers.ssrn.com/sol3/Delivery.cfm/5334569.pdf?abstractid=5334569&mirid=1","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"imbalance-prime-sieving-every-prime-gap-is-a","repo_url":"https://github.com/sydx/imbalance_prime_sieve","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}