{"paper":{"title":"Best possible densities of Dickson m-tuples, as a consequence of Zhang-Maynard-Tao","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Andrew Granville, Daniel M. Kane, Dimitris Koukoulopoulos, Robert J. Lemke Oliver","submitted_at":"2014-10-29T23:36:14Z","abstract_excerpt":"We determine for what proportion of integers $h$ one now knows that there are infinitely many prime pairs $p,\\ p+h$ as a consequence of the Zhang-Maynard-Tao theorem. We consider the natural generalization of this to $k$-tuples of integers, and we determine the limit of what can be deduced assuming only the Zhang-Maynard-Tao theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8198","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}