{"paper":{"title":"Sampling Goldbach Numbers at Random","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.NT","authors_text":"Ljuben Mutafchiev","submitted_at":"2015-08-05T21:09:21Z","abstract_excerpt":"Let $\\Sigma_{2n}$ be the set of all partitions of the even integers from the interval $(4,2n], n>2,$ into two odd prime parts. We select a partition from the set $\\Sigma_{2n}$ uniformly at random. Let $2G_n$ be the number partitioned by this selection. $2G_n$ is sometimes called a Goldbach number. In [6] we showed that $G_n/n$ converges weakly to the maximum $T$ of two random variables which are independent copies of a uniformly distributed random variable in the interval $(0,1)$. In this note we show that the mean and the variance of $G_n/n$ tend to the mean $\\mu_T=2/3$ and variance $\\sigma_T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04457","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"}