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It is known that $D(N)$ can be bounded above by $$ D(N) \\leq C^* \\Theta(N), \\quad \\Theta(N):= \\frac{N}{\\log^2 N}\\prod_{\\substack{p|N p>2}} \\left( 1 + \\frac{1}{p-2}\\right)\\prod_{p>2}\\left(1-\\frac{1}{(p-1)^2}\\right) $$ where $C^*$ denotes Chen's constant. It is conjectured that $C^*=2$. In 2004, Wu showed that $C^* \\leq 7.8209$. We attempted to replicate his work in computing Chen's constant, and in doing so we provide an imp"},"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":"1801.01813","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2017-12-29T03:16:47Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"6d1f7966c10c770a0935e17596f590b84697549af8dce4de54104f533fdc32f5","abstract_canon_sha256":"0289135547511ff6728a696479abcdfd7a591e401ff877466beeeb0528c49fa5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:40.919915Z","signature_b64":"LvoELGxVU8FoL5ygODJ6+MUUliPATmzy7hD7CtSkBPxgdAnbmsvdczpCWX1oqq79WVxqGYlUZiGP1gNa2ZuRAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f6bc699c46478035425429dd5608b2bd901c313196652fcd2e2a04e2b739dcb","last_reissued_at":"2026-05-18T00:26:40.919214Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:40.919214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a numerical upper bound for the extended Goldbach conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.HO","authors_text":"David Quarel","submitted_at":"2017-12-29T03:16:47Z","abstract_excerpt":"The Goldbach conjecture states that every even number can be decomposed as the sum of two primes. Let $D(N)$ denote the number of such prime decompositions for an even $N$. It is known that $D(N)$ can be bounded above by $$ D(N) \\leq C^* \\Theta(N), \\quad \\Theta(N):= \\frac{N}{\\log^2 N}\\prod_{\\substack{p|N p>2}} \\left( 1 + \\frac{1}{p-2}\\right)\\prod_{p>2}\\left(1-\\frac{1}{(p-1)^2}\\right) $$ where $C^*$ denotes Chen's constant. It is conjectured that $C^*=2$. In 2004, Wu showed that $C^* \\leq 7.8209$. 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