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A sequence of polynomials $f_1(x), f_2(x), ...$, such that $f_i(x)\\in \\Z[x]$, $"},"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":"1104.1579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-04-08T14:01:41Z","cross_cats_sorted":[],"title_canon_sha256":"1deebd61882a8aba59da1048a81eec3822162ca1a7c29a5d87b0d702553a34f8","abstract_canon_sha256":"0851b84054085430ac66a43b859e6d4cd58c95c1eaf1b1b0aa26bec7939bb3db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:44.818096Z","signature_b64":"M7ez69QIVEG7Ll8bWqqt4Nj/KWGY58XUV8F5uNYdNn6MopaA61Du8SP8nRGRnks7iVgCL/LuSKzj4QZ2NlMIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc23212379a9da2720ea5b98e100df6e7014fa1e986539d13afeed292c329f74","last_reissued_at":"2026-05-18T04:24:44.817654Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:44.817654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomial Cunningham Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lenny Jones","submitted_at":"2011-04-08T14:01:41Z","abstract_excerpt":"Let $\\epsilon\\in \\{-1,1\\}$. A sequence of prime numbers $p_1, p_2, p_3, ...$, such that $p_i=2p_{i-1}+\\epsilon$ for all $i$, is called a {\\it Cunningham chain} of the first or second kind, depending on whether $\\epsilon =1$ or -1 respectively. If $k$ is the smallest positive integer such that $2p_k+\\epsilon$ is composite, then we say the chain has length $k$. Although such chains are necessarily finite, it is conjectured that for every positive integer $k$, there are infinitely many Cunningham chains of length $k$. 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