{"paper":{"title":"On the Distribution of the Number of Goldbach Partitions of a Randomly Chosen Positive Even Integer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ljuben Mutafchiev","submitted_at":"2016-02-03T09:28:54Z","abstract_excerpt":"Let $\\mathcal{P}=\\{p_1,p_2,...\\}$ be the set of all odd primes arranged in increasing order. A Goldbach partition of the even integer $2k>4$ is a way of writing it as a sum of two primes from $\\mathcal{P}$ without regard to order. Let $Q(2k)$ be the number of all Goldbach partitions of the number $2k$. Assume that $2k$ is selected uniformly at random from the interval $(4,2n], n>2$, and let $Y_n=Q(2k)$ with probability $1/(n-2)$. We prove that the random variable $\\frac{Y_n}{n/\\left(\\frac{1}{2}\\log{n}\\right)^2}$ converges weakly, as $n\\to\\infty$, to a uniformly distributed random variable in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01232","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"}