{"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/improved-upper-bound-on-brun-s-constant-under","title":"Improved Upper Bound on Brun's Constant Under GRH","arxiv_id":"2504.15658","date":"2025-04-22","proceeding":null,"authors":["Lachlan Dunn"],"abstract":"Brun's constant is the summation of the reciprocals of all twin primes, given by $B=\\sum_{p \\in P_2}{\\left( \\frac{1}{p} + \\frac{1}{p+2}\\right)}$. While rigorous unconditional bounds on $B$ are known, we present the first rigorous bound on Brun's constant under the GRH assumption, yielding $B < 2.1594$.","url_abs":"https://arxiv.org/abs/2504.15658v2","url_pdf":"https://arxiv.org/pdf/2504.15658v2.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":"improved-upper-bound-on-brun-s-constant-under","repo_url":"https://github.com/lachlanjdunn/b_under_grh","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}