{"paper":{"title":"An intermediate conjecture between Goldbach and Dubner: every even number is the sum of a prime and a twin prime","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tushar Pandey","submitted_at":"2026-08-03T15:25:12Z","abstract_excerpt":"Call a prime $t$ a twin member if $t-2$ or $t+2$ is prime, and let $\\mathcal{T}$ denote the set of twin members. We study the statement (S): every even $n \\ge 6$ can be written as $n = p + t$ with $p$ prime and $t \\in \\mathcal{T}$. Statement (S) sits between the Goldbach conjecture and Dubner's conjecture (every even $n > 4208$ is a sum of two twin members), and we observe that (S) is a single elementary statement implying both the Goldbach conjecture and the twin prime conjecture. We prove an orientation-rigidity theorem: for $n \\not\\equiv 0 \\pmod 3$, all twin members $t$ appearing in Goldbac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02381","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.02381/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}