{"paper":{"title":"Topological properties and algebraic independence of sets of prime-representing constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.NT","authors_text":"Kota Saito, Wataru Takeda","submitted_at":"2021-12-29T03:31:38Z","abstract_excerpt":"Let $(c_k)_{k\\in \\mathbb{N}}$ be a sequence of positive integers. We investigate the set of $A>1$ such that the integer part of $A^{c_1\\cdots c_k}$ is always a prime number for every positive integer $k$. Let $\\mathcal{W}(c_k)$ be this set. The first goal of this article is to determine the topological structure of $\\mathcal{W}(c_k)$. Under some conditions on $(c_k)_{k\\in \\mathbb{N}}$, we reveal that $\\mathcal{W}(c_k)\\cap [0,a]$ is homeomorphic to the Cantor middle third set for some $a$. The second goal is to propose an algebraically independent subset of $\\mathcal{W}(c_k)$ if $c_k$ is rapidl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.14383","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.14383/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"}