{"schema_version":"source-reader-v1","record":{"source_id":"openmath-prime-note","versions":[{"id":"openmath-prime-note@a640f3adfa536da0","source_id":"openmath-prime-note","title":"OpenMath · prime note","owner":"OpenMath staff","url":"https://openmath.dev/sources/prime-note","subject_scope":"Elementary-number-theory reference prose","revision":"a640f3adfa536da0","content_sha256":"a640f3adfa536da0fb792b52610d9d9d56540fbeb430df766667a4ff65b8b49f","update_method":"Manual checked import; new observations require staff preview and publication","identifier_policy":"Canonical source URL plus explicit item/declaration locator; no fuzzy identity merge","observed_on":"2026-10-01","source_updated_on":"2026-09-26","rights":"full-text","license":"CC-BY-4.0","terms_url":"https://creativecommons.org/licenses/by/4.0/","attribution":"OpenMath staff","rights_note":"Licensed source links and exact source spans; attribution retained.","check_interval_days":180}],"entries":[{"id":"prime-infinitude:entry:0:v1","source_version_id":"openmath-prime-note@a640f3adfa536da0","item_id":"notes/primes.md lines 9–15, 21–29","url":"https://openmath.dev/sources/prime-note","wording":"For every natural number n, does there exist a prime p with n < p?","wording_kind":"paraphrase","locator":"notes/primes.md lines 9–15, 21–29","supersedes":null}],"problems":[{"slug":"prime-infinitude","title":"Why are there infinitely many primes?","publication_version":8}],"selected_version_id":"openmath-prime-note@a640f3adfa536da0","available_versions":[{"id":"openmath-prime-note@a640f3adfa536da0","revision":"a640f3adfa536da0","observed_on":"2026-10-01","title":"OpenMath · prime note","publication":null,"content_sha256":"a640f3adfa536da0fb792b52610d9d9d56540fbeb430df766667a4ff65b8b49f","used_in_current_publications":true}],"usages":[{"id":"source-use-004ea756488ca6c0afc2","entry_id":"prime-infinitude:entry:0:v1","problem":{"slug":"prime-infinitude","title":"Why are there infinitely many primes?","publication_version":8},"kind":"assessment","title":"Known theorem in authored reference note","claim":{"id":"claim-primes-unbounded","version":3,"slug":"primes-unbounded","title":"The set of primes is unbounded"},"fragment":"claim-primes-unbounded","assessment":{"id":"prime-infinitude:report:0:v1","entry_id":"prime-infinitude:entry:0:v1","state":"resolved","source_label":"Known theorem in authored reference note","scope":"The cited source item and version only; this is not an independent OpenMath assessment.","source_date":null,"observed_on":"2026-10-01","evidence_url":"https://openmath.dev/sources/prime-note","supersedes":null},"superseded":false,"formalization":null,"update":null},{"id":"source-use-36519fe17d5c26e398f5","entry_id":"prime-infinitude:entry:0:v1","problem":{"slug":"prime-infinitude","title":"Why are there infinitely many primes?","publication_version":8},"kind":"assessment","title":"Known theorem in authored reference note","claim":{"id":"claim-primes-infinite","version":3,"slug":"primes-infinite","title":"There are infinitely many primes"},"fragment":"claim-primes-infinite","assessment":{"id":"prime-infinitude:report:0:v1","entry_id":"prime-infinitude:entry:0:v1","state":"resolved","source_label":"Known theorem in authored reference note","scope":"The cited source item and version only; this is not an independent OpenMath assessment.","source_date":null,"observed_on":"2026-10-01","evidence_url":"https://openmath.dev/sources/prime-note","supersedes":null},"superseded":false,"formalization":null,"update":null},{"id":"source-use-c8e15d37272d328a4b64","entry_id":"prime-infinitude:entry:0:v1","problem":{"slug":"prime-infinitude","title":"Why are there infinitely many primes?","publication_version":8},"kind":"assessment","title":"Known theorem in authored reference note","claim":{"id":"claim-prime-strictly-above","version":3,"slug":"prime-strictly-above","title":"A prime strictly above every bound"},"fragment":"claim-prime-strictly-above","assessment":{"id":"prime-infinitude:report:0:v1","entry_id":"prime-infinitude:entry:0:v1","state":"resolved","source_label":"Known theorem in authored reference note","scope":"The cited source item and version only; this is not an independent OpenMath assessment.","source_date":null,"observed_on":"2026-10-01","evidence_url":"https://openmath.dev/sources/prime-note","supersedes":null},"superseded":false,"formalization":null,"update":null},{"id":"source-use-c16e597b6c1d0f25e2f1","entry_id":"prime-infinitude:entry:0:v1","problem":{"slug":"prime-infinitude","title":"Why are there infinitely many primes?","publication_version":8},"kind":"definition","title":"Unbounded primes","claim":null,"fragment":"question","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-a06d3c574cdd0ed04d43","entry_id":"prime-infinitude:entry:0:v1","problem":{"slug":"prime-infinitude","title":"Why are there infinitely many primes?","publication_version":8},"kind":"question","title":"Why are there infinitely many primes?","claim":null,"fragment":"question","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-13f6bb2170e5f1d8ccab","entry_id":"prime-infinitude:entry:0:v1","problem":{"slug":"prime-infinitude","title":"Why are there infinitely many primes?","publication_version":8},"kind":"reading","title":"Read the setting and notation before comparing the results.","claim":null,"fragment":"provenance","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-3661e974f3ad0bbeaba8","entry_id":"prime-infinitude:entry:0:v1","problem":{"slug":"prime-infinitude","title":"Why are there infinitely many primes?","publication_version":8},"kind":"statement","title":"A prime strictly above every bound","claim":{"id":"claim-prime-strictly-above","version":3,"slug":"prime-strictly-above","title":"A prime strictly above every bound"},"fragment":"claim-prime-strictly-above","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-4d78a20adcf7cbb98f0b","entry_id":"prime-infinitude:entry:0:v1","problem":{"slug":"prime-infinitude","title":"Why are there infinitely many primes?","publication_version":8},"kind":"statement","title":"The set of primes is unbounded","claim":{"id":"claim-primes-unbounded","version":3,"slug":"primes-unbounded","title":"The set of primes is unbounded"},"fragment":"claim-primes-unbounded","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-e2d8b206f47fd8551b11","entry_id":"prime-infinitude:entry:0:v1","problem":{"slug":"prime-infinitude","title":"Why are there infinitely many primes?","publication_version":8},"kind":"statement","title":"There are infinitely many primes","claim":{"id":"claim-primes-infinite","version":3,"slug":"primes-infinite","title":"There are infinitely many primes"},"fragment":"claim-primes-infinite","assessment":null,"superseded":false,"formalization":null,"update":null}],"linked_entries":[],"linked_sources":[]}}