{"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/12103829","title":"First occurrences of square-free gaps and an algorithm for their computation","arxiv_id":"1210.3829","date":"2012-10-14","proceeding":null,"authors":["Louis Marmet"],"abstract":"This paper reports the results of a search for first occurrences of square-free gaps using an algorithm based on the sieve of Eratosthenes. Using Qgap(L) to denote the starting number of the first gap having exactly the length L, the following values were found since August 1999: Qgap(10)=262315467, Qgap(12)=47255689915, Qgap(13)=82462576220, Qgap(14)=1043460553364, Qgap(15)=79180770078548, Qgap(16)=3215226335143218, Qgap(17)=23742453640900972 and Qgap(18)=125781000834058568. No gaps longer than 18 were found up to N=125870000000000000.","url_abs":"http://arxiv.org/abs/1210.3829v1","url_pdf":"http://arxiv.org/pdf/1210.3829v1.pdf","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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"12103829","repo_url":"https://github.com/sikefield3/double-square","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}