{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-11T05:41:46Z",
    "providers": [
      "Claude"
    ],
    "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify",
    "pass": 2,
    "wave": 1,
    "engine": "claude",
    "enrichment": {
      "pass": 3,
      "engine": "claude",
      "producedAt": "2026-10-05T16:30:00Z",
      "ingestedAt": "2026-10-05T13:22:32+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:52:00+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q49008",
    "registryId": "vr.tr.prime-number",
    "name": "prime number",
    "version": "0.2.0-wave.1",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QTY"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q49008/",
  "model": {
    "registry_id": "vr.tr.prime-number",
    "name": "prime number",
    "purpose": "Let an agent handle primes mathematically, with tests, notable classes and records, and their role in cryptography.",
    "definition": "A natural number greater than 1 that has no positive divisors other than 1 and itself, such as 2, 3, 5, 7 and 11.",
    "what_it_is_for": "Primes are the building blocks of integers and underpin much of number theory and public-key cryptography.",
    "affordances": [
      "test primality",
      "factor composite numbers into primes",
      "search for large primes, such as Mersenne primes",
      "use them, in cryptographic keys"
    ],
    "distinguishing_features": [
      "Exactly two positive divisors",
      "Infinitely many exist",
      "2 is the only even prime",
      "Primality tests may be probabilistic or proven"
    ],
    "appearance": "Numbers; notable primes are listed in tables and records.",
    "visual_identification": [
      "Divisible only by 1 and itself",
      "Notation for special classes such as Mersenne primes 2^p - 1",
      "Records such as the largest known prime"
    ],
    "physical_properties": [
      {
        "quantity": "primes below 100",
        "typical_range": "25",
        "unit": "count",
        "note": ""
      },
      {
        "quantity": "largest known prime digits",
        "typical_range": "over 41 million",
        "unit": "digits",
        "note": "a Mersenne prime found in 2024"
      }
    ],
    "families_and_kinds": [
      "Mersenne and double Mersenne primes",
      "twin primes",
      "palindromic primes",
      "titanic and gigantic primes by size",
      "provable versus probable primes"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "integer",
        "why": "natural number"
      },
      {
        "relation": "is used in",
        "target": "cryptographic key",
        "why": "RSA"
      },
      {
        "relation": "is studied by",
        "target": "mathematics",
        "why": "number theory"
      },
      {
        "relation": "is confused with",
        "target": "odd number",
        "why": "not all odd numbers are prime"
      }
    ],
    "identifiers": [
      {
        "scheme": "OEIS A000040",
        "value_or_pattern": "sequence of primes",
        "note": "reference"
      }
    ],
    "standards_and_regulation": [
      "FIPS 186 prime generation requirements for cryptography"
    ],
    "failure_modes_and_hazards": [
      "Using probable primes where proof is required",
      "Weak primes in cryptography",
      "Off-by-one errors in counting primes"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Test primality and factorise numbers with stated algorithms.",
        "Explain properties of primes and their use in cryptography in general terms."
      ],
      "must_not": [
        "Use factorisation to break encryption protecting others' data without authority.",
        "Present conjectures as proven theorems.",
        "Claim discoveries without verification."
      ],
      "requires_human": [
        "Publishing results that weaken widely used cryptography."
      ]
    },
    "ethics": {
      "considerations": [
        "Primes underpin encryption that protects privacy and money.",
        "Mathematical credit should go to the right people."
      ],
      "affected_parties": [
        "Users of encrypted systems",
        "Mathematicians"
      ]
    },
    "owners": {
      "steward": "Nobody: a mathematical object held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q49008: prime number",
      "url": "https://www.wikidata.org/wiki/Q49008",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Prime number",
      "url": "https://en.wikipedia.org/wiki/Prime_number",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "definition",
        "name": "Definition",
        "description": "What is a prime.",
        "rationale": "The definition is exact.",
        "layers": [
          {
            "id": "test",
            "name": "Primality",
            "description": "Is it prime.",
            "findings": [
              {
                "id": "test-finding",
                "name": "Primality",
                "description": "Primality result.",
                "questions": [
                  {
                    "text": "Is this number prime, by which test?",
                    "kind": "measurement"
                  },
                  {
                    "text": "Is the result proven or probabilistic?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "factorisation",
            "name": "Factorisation",
            "description": "Prime factors.",
            "findings": [
              {
                "id": "factorisation-finding",
                "name": "Factors",
                "description": "Prime factorisation.",
                "questions": [
                  {
                    "text": "What is the prime factorisation of this number?",
                    "kind": "measurement"
                  },
                  {
                    "text": "How long does factoring take at this size?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "classes",
        "name": "Classes",
        "description": "Special primes.",
        "rationale": "Classes have their own properties.",
        "layers": [
          {
            "id": "class",
            "name": "Class",
            "description": "Mersenne, twin, palindromic.",
            "findings": [
              {
                "id": "class-finding",
                "name": "Class",
                "description": "Class membership.",
                "questions": [
                  {
                    "text": "Does it belong to a special class?",
                    "kind": "definition"
                  },
                  {
                    "text": "What defines that class?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          },
          {
            "id": "records",
            "name": "Records",
            "description": "Largest known.",
            "findings": [
              {
                "id": "records-finding",
                "name": "Records",
                "description": "Record status.",
                "questions": [
                  {
                    "text": "What is the largest known prime of this class?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Who verified it?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "theory",
        "name": "Theory",
        "description": "Distribution and conjectures.",
        "rationale": "Theorems and conjectures must be kept apart.",
        "layers": [
          {
            "id": "distribution",
            "name": "Distribution",
            "description": "Prime number theorem.",
            "findings": [
              {
                "id": "distribution-finding",
                "name": "Distribution",
                "description": "How primes are distributed.",
                "questions": [
                  {
                    "text": "How many primes are there below n, approximately?",
                    "kind": "measurement"
                  },
                  {
                    "text": "Which theorem gives that?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "conjectures",
            "name": "Conjectures",
            "description": "Open problems.",
            "findings": [
              {
                "id": "conjectures-finding",
                "name": "Conjectures",
                "description": "Open problems.",
                "questions": [
                  {
                    "text": "Is this statement proven or a conjecture?",
                    "kind": "boundary"
                  },
                  {
                    "text": "What is known partially?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "cryptography",
        "name": "Cryptography",
        "description": "Use in keys.",
        "rationale": "Primes secure communications.",
        "layers": [
          {
            "id": "keys",
            "name": "Keys",
            "description": "Prime generation.",
            "findings": [
              {
                "id": "keys-finding",
                "name": "Key generation",
                "description": "Prime generation for keys.",
                "questions": [
                  {
                    "text": "How are primes generated for keys?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which standard applies?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "strength",
            "name": "Strength",
            "description": "Size and safety.",
            "findings": [
              {
                "id": "strength-finding",
                "name": "Strength",
                "description": "Security of prime sizes.",
                "questions": [
                  {
                    "text": "Are these primes large enough for current security?",
                    "kind": "boundary"
                  },
                  {
                    "text": "What does quantum computing change?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should prime classes be separate entries?",
    "How should record primes be tracked?",
    "How should agents present unproven conjectures such as the twin prime conjecture?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}