{ "model": { "rank": 1383, "code": "thing-q49008", "model_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.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QTY", "industry": "", "version": "", "url": "/models/thing/q49008/", "tier": 2, "score": 151, "payload": { "layer": "wikidata", "aliases": [ "largest known prime number", "titanic prime", "gigantic prime", "provable prime", "palindromic prime", "double Mersenne prime", "Mersenne prime", "repunit prime", "Wieferich prime", "Fermat prime", "Proth prime", "illegal prime", "primes in arithmetic progression", "widely digitally delicate prime", "cluster prime", "Fibonacci prime", "twin prime", "prime factor", "sexy prime", "irregular prime", "Truncatable prime", "Jacob prime number", "Pi prime", "cuban prime", "good prime", "Bi-twin chain", "supersingular prime", "Wilson prime", "balanced prime", "Newman–Shanks–Williams prime", "primorial prime", "Strong prime", "delicate prime", "safe prime", "Chen prime", "Wolstenholme prime", "Pythagorean prime", "unique prime", "Wagstaff prime", "Pillai prime" ], "aliasCount": 58, "merged": 59, "knownIn": 151, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.prime-number", "source": { "dataset": "wikidata", "item": "Q49008", "url": "https://www.wikidata.org/wiki/Q49008", "license": "CC0 1.0" } }, "research": { "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" }, "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": [] }, "sources": [], "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 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "unit, quantity or measure", "method": "Written from the archetype playbook - what this kind of thing needs beyond identity and provenance - and from the structure that recurred across 6,333 models already researched by two engines. Applied to this entry by rule. No source was read for this thing and no claim here is researched. This entry carries no facets of its own, so they were inferred from its domain - a guess about a whole domain applied to one thing.", "facetsInferred": true, "nextPass": "A researcher replaces this draft with a sourced specification. Treat every sentence below as a proposal to argue with.", "purpose": "Give an agent a durable, checkable way to recognise a prime number, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent handle primes mathematically, with tests, notable classes and records, and their role in cryptography.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: largest known prime number, titanic prime, gigantic prime, provable prime, palindromic prime, double Mersenne prime, Mersenne prime, repunit prime, Wieferich prime, Fermat prime, Proth prime, illegal prime.", "59 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 151 Wikipedia languages, which is a measure of how widely the thing is known, not of how important it is." ], "openQuestionsForResearch": [ "Which of the bundles below does a real task actually need, and which are ceremony?", "What does this thing have that the facets do not capture at all?", "Which neighbouring kind is most often confused with a prime number, and on what evidence are they told apart?" ], "whatItIsMadeOf": "an abstraction with no physical instance", "physicalCharacter": [ "Does nothing on its own; everything it does, something else did to it.", "These come from the domain this entry sits in rather than from the entry itself, so treat them as a first guess about the whole domain applied to one thing." ], "whatCanBeDoneWithIt": [ "observe it, measure it, record its state" ], "howItIsRecognised": [ "Nothing to see: a unit is a convention. What is seen is an instrument reading in it." ], "relatedModels": [ { "relation": "covers", "note": "Finer kinds folded into this entry because telling them apart needs a task that asks for it. Each is a model waiting to be split out when one does.", "targets": [ "largest known prime number", "titanic prime", "gigantic prime", "provable prime", "palindromic prime", "double Mersenne prime", "Mersenne prime", "repunit prime", "Wieferich prime", "Fermat prime", "Proth prime", "illegal prime" ] } ], "standing": "Described in 151 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 59 finer distinctions are held inside this entry as names rather than as separate models.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one prime number from another, and a prime number from things that resemble it.", "rationale": "Recognition comes before every other claim. Without stable identity nothing else in the model can be trusted to be about the same thing twice.", "layers": [ { "id": "naming-and-identifiers", "name": "Names and identifiers", "description": "The names this thing goes by and the identifiers that survive translation and time.", "findings": [ { "id": "preferred-name-and-aliases", "name": "Preferred name, aliases and local names", "description": "Which name to use, which names mean the same thing, and which merely sound similar.", "questions": [ { "id": "preferred-name-and-aliases-q01", "text": "What identifies and describes the name of a prime number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "preferred-name-and-aliases-q02", "text": "Who or what asserted this about the name of a prime number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "preferred-name-and-aliases-q03", "text": "What may an agent decide or do once the name of a prime number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "stable-identifiers", "name": "Stable identifiers and external keys", "description": "Identifiers that keep pointing at this kind of thing across systems and languages.", "questions": [ { "id": "stable-identifiers-q01", "text": "What identifies and describes an identifier for a prime number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stable-identifiers-q02", "text": "Who or what asserted this about an identifier for a prime number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stable-identifiers-q03", "text": "What may an agent decide or do once an identifier for a prime number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "classification-and-granularity", "name": "Classification and granularity", "description": "Where a prime number sits among kinds, and how finely a task needs to cut it.", "findings": [ { "id": "kind-and-parents", "name": "Kind, parents and neighbouring kinds", "description": "The classes this thing belongs to and the ones it is next to.", "questions": [ { "id": "kind-and-parents-q01", "text": "What identifies and describes the kind of a prime number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "kind-and-parents-q02", "text": "Who or what asserted this about the kind of a prime number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "kind-and-parents-q03", "text": "What may an agent decide or do once the kind of a prime number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "distinguishing-features", "name": "Distinguishing features", "description": "What separates a prime number from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a prime number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "distinguishing-features-q02", "text": "Who or what asserted this about what distinguishes a prime number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "distinguishing-features-q03", "text": "What may an agent decide or do once what distinguishes a prime number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "state-and-lifecycle", "name": "State and lifecycle", "description": "The states a prime number passes through and the events that move it between them.", "rationale": "Most decisions about a thing depend on what state it is in now, which is a claim with a time on it, not a property.", "layers": [ { "id": "lifecycle-stages", "name": "Lifecycle stages", "description": "From coming into existence to ceasing to be one of these.", "findings": [ { "id": "stages-and-transitions", "name": "Stages and transitions", "description": "The stages worth naming and what moves a prime number between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a prime number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stages-and-transitions-q02", "text": "Who or what asserted this about the lifecycle of a prime number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stages-and-transitions-q03", "text": "What may an agent decide or do once the lifecycle of a prime number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "observations-and-status", "name": "Observations and current status", "description": "What is observed about a prime number, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a prime number is recorded so that it can be superseded rather than overwritten.", "questions": [ { "id": "observation-record-q01", "text": "What identifies and describes an observation of a prime number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "observation-record-q02", "text": "Who or what asserted this about an observation of a prime number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "observation-record-q03", "text": "What may an agent decide or do once an observation of a prime number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "definition-and-realisation", "name": "Definition, dimension and realisation", "description": "What prime number is defined as and how it is realised in practice.", "rationale": "A unit is not the quantity it measures, and its definition has a history that older data still depends on.", "layers": [ { "id": "definition", "name": "Definition and dimension", "description": "The defining relation and the quantity it measures.", "findings": [ { "id": "definition-record", "name": "Definition, body and date", "description": "What defines it now, and what defined it before.", "questions": [ { "id": "definition-record-q01", "text": "How is prime number defined, by which body, and since when?", "kind": "definition" }, { "id": "definition-record-q02", "text": "What was the previous definition, and what data still depends on it?", "kind": "provenance" } ] } ] }, { "id": "conversion", "name": "Conversion and compatibility", "description": "Relations to other units, exact or approximate.", "findings": [ { "id": "conversion-record", "name": "Conversions and their exactness", "description": "Factors, and whether each is exact by definition.", "questions": [ { "id": "conversion-record-q01", "text": "What conversions relate prime number to other units, and which are exact by definition?", "kind": "measurement" }, { "id": "conversion-record-q02", "text": "Where does rounding a conversion change a decision, and how should that be recorded?", "kind": "action" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a prime number came from and when it held.", "rationale": "A claim without a source and a time cannot be superseded, only overwritten, and an agent that overwrites loses the ability to explain itself.", "layers": [ { "id": "source-and-authority", "name": "Source and authority", "description": "Who said it, on what evidence, and how strongly.", "findings": [ { "id": "claim-provenance", "name": "Claim provenance and confidence", "description": "The authority behind each claim about a prime number and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a prime number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "claim-provenance-q02", "text": "Who or what asserted this about a claim about a prime number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "claim-provenance-q03", "text": "What may an agent decide or do once a claim about a prime number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "time-and-versions", "name": "Time, versions and supersession", "description": "When a claim was true, when it was learnt, and what replaced it.", "findings": [ { "id": "validity-and-supersession", "name": "Validity period and supersession", "description": "How an old claim about a prime number is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a prime number, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "validity-and-supersession-q02", "text": "Who or what asserted this about the validity of a claim about a prime number, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "validity-and-supersession-q03", "text": "What may an agent decide or do once the validity of a claim about a prime number is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] } ] }, "statistics": { "bundles": 4, "layers": 8, "findings": 10, "questions": 28 } } } }