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We establish unconditionally that there is an infinite sequence $\\{p_n\\}_{n \\in \\mathbb{N}}$ of increasing primes and a randomized algorithm $A$ running in expected sub-exponential time such that for each $n$, on input $1^{|p_n|}$, $A$ outputs $p_n$ with probability $1$. In other words, our result provides a pseudodeterministic construction of primes in sub-exponential time which works infinitely often.\n  This result follows from a much more general theorem about ps"},"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":"1612.01817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-12-06T14:20:41Z","cross_cats_sorted":["cs.DM","cs.DS","math.CO","math.NT"],"title_canon_sha256":"5d675e2b0e62070f48460d232d013101b84fc2aac785ddd8209a7b5292455a0f","abstract_canon_sha256":"f0696c3d4dfa2b0acd984428e19d5c6cafd243fd43e397527e73c51e74c856b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:47.543161Z","signature_b64":"yvxcSo9hDA/1zXtQrY15NQcszVZhnVjwv6V4mtlapaYXdSjuJwMBdhhiA+ggI029lq8elO4gMJS70Ue7AkP/BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"653975cae78ac3c4185603903c4f0008c029543cab6477541e1ae773f40dd306","last_reissued_at":"2026-05-18T00:55:47.542643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:47.542643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pseudodeterministic Constructions in Subexponential Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS","math.CO","math.NT"],"primary_cat":"cs.CC","authors_text":"Igor C. Oliveira, Rahul Santhanam","submitted_at":"2016-12-06T14:20:41Z","abstract_excerpt":"We study pseudodeterministic constructions, i.e., randomized algorithms which output the same solution on most computation paths. We establish unconditionally that there is an infinite sequence $\\{p_n\\}_{n \\in \\mathbb{N}}$ of increasing primes and a randomized algorithm $A$ running in expected sub-exponential time such that for each $n$, on input $1^{|p_n|}$, $A$ outputs $p_n$ with probability $1$. 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