{"paper":{"title":"Gaps of Smallest Possible Order between Primes in an Arithmetic Progression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Liangyi Zhao, Roger C. Baker","submitted_at":"2014-12-01T18:29:52Z","abstract_excerpt":"Let $t \\in \\mathbb{N}$, $\\eta >0$. Suppose that $x$ is a sufficiently large real number and $q$ is a natural number with $q \\leq x^{5/12-\\eta}$, $q$ not a multiple of the conductor of the exceptional character $\\chi^*$ (if it exists). Suppose further that, \\[ \\max \\{p : p | q \\} < \\exp (\\frac{\\log x}{C \\log \\log x}) \\; \\; {and} \\; \\; \\prod_{p | q} p < x^{\\delta}, \\] where $C$ and $\\delta$ are suitable positive constants depending on $t$ and $\\eta$. Let $a \\in \\mathbb{Z}$, $(a,q)=1$ and \\[ \\mathcal{A} = \\{n \\in (x/2, x]: n \\equiv a \\pmod{q} \\} . \\] We prove that there are primes $p_1 < p_2 < .."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0574","kind":"arxiv","version":4},"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"}