{"paper":{"title":"Goldbach for Gaussian, Hurwitz, Octavian and Eisenstein primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.NT","authors_text":"Oliver Knill","submitted_at":"2016-06-20T02:34:36Z","abstract_excerpt":"We formulate Goldbach type questions for Gaussian, Hurwitz, Octavian and Eisenstein primes. They are different from Goldbach type statements by Takayoshi Mitsui from 1960 for number fields or C.A. Holben and James Jordan from 1968 for Gaussian integers. Here is what we meeasure: 1) Every even Gaussian integer a+ib satisfying a>2, b>2 is a sum of two Gaussian primes with positive coefficients. 2) Every Eisenstein integer a+bw with a>3,b>3 and w=(1+sqrt(-3))/2 is the sum of two Eisenstein primes with positive coefficients. Note that no evenness condition is asked in the Eisenstein case. 3) Every"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05958","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"}