{"paper":{"title":"Redefining Euler-Rabinowitsch Polynomials with Heegner Number Based Quadratic Formulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Neha Mishra, Shipra Kumari, Sudarshan Kumaresan","submitted_at":"2025-08-04T18:44:56Z","abstract_excerpt":"This paper introduces a novel class of prime-generating quadratic polynomials defined by $f_{Z,k,H}(n) = n^2 - (2Zk - 1)n + \\frac{(2Zk - 1)^2 + H}{4}$, where $Zk \\in \\mathbb{Z}_{\\geq 0}$ and $H$ belongs to the set of Heegner numbers. This form is closely related to the Euler-Rabinowitsch polynomials through specific substitutions. The structure enables algebraic tuning for prime-rich outputs and provides deeper insight into the impact of Heegner numbers on prime distribution. Using tools such as the Bateman-Horn conjecture and prime-counting functions, we demonstrate that this family can be op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.02821","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/2508.02821/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"}