{"paper":{"title":"Prime-Residue-Class of Uniform Charges on the Integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Joseph B. Kadane, Michael Spece","submitted_at":"2018-09-19T15:27:53Z","abstract_excerpt":"There is a probability charge on the power set of the integers that gives probability $1/p$ to every residue class modulo a prime $p$. There exists such a charge that gives probability $w$ to the set of prime numbers iff $w \\in [0,1/2]$. Similarly, there is such a charge that gives probability $x$ to a residue class modulo $c$, where $c$ is composite, iff $x \\in [0,1/y]$, where $y$ is the largest prime factor of $c$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07244","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":""},"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"}