{"paper":{"title":"Strong pseudoprimes to the first 9 prime bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yingpu Deng, Yupeng Jiang","submitted_at":"2012-06-30T09:13:17Z","abstract_excerpt":"Define $\\psi_m$ to be the smallest strong pseudoprime to the first $m$ prime bases. The exact value of $\\psi_m$ is known for $1\\le m \\le 8$. Z. Zhang have found a 19-decimal-digit number $Q_{11}=3825\\,12305\\,65464\\,13051$ which is a strong pseudoprime to the first 11 prime bases and he conjectured that $$\\psi_9=\\psi_{10}=\\psi_{11}=Q_{11}.$$ We prove the conjecture by algorithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0063","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"}