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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1207.0063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-06-30T09:13:17Z","cross_cats_sorted":[],"title_canon_sha256":"8b1d7c33f61d707881e727143cae610dcc992b263f512d8bc25028bb28fac09f","abstract_canon_sha256":"aeed764df622225e8145c1a053e78020acfebef97cd194089a20b20240baaeaf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:00.433121Z","signature_b64":"DGDFJDwv5I64kAOCKtYVpH4ye3f7a059u+n01ZVjxFTFOjugO9I3GUufjRLW2r8Siy4KX4NN0GH6rZCzKMFlDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b41cc61cb5f09e430a3430167bf9cf1b87c2695040bb88d0b1d8d5f7e482ac68","last_reissued_at":"2026-05-18T03:52:00.432447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:00.432447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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