{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.prime-number","code":"thing-q49008","url":"https://ver.cy/models/thing/q49008/","name":"prime number","alternateNames":["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"],"kind":"thing","status":"published","version":"0.2.0-wave.1","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QTY"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A natural number greater than 1 that has no positive divisors other than 1 and itself, such as 2, 3, 5, 7 and 11.","purpose":"Let an agent handle primes mathematically, with tests, notable classes and records, and their role in cryptography.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Exactly two positive divisors","Infinitely many exist","2 is the only even prime","Primality tests may be probabilistic or proven"],"structure":{"bundles":[{"id":"definition","name":"Definition","description":"What is a prime.","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 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number"},{"target":"cryptographic key","type":"related","note":"RSA"},{"target":"mathematics","type":"related","note":"number theory"},{"target":"odd number","type":"related","note":"not all odd numbers are prime"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.prime-number","Wikidata: Q49008 (https://www.wikidata.org/wiki/Q49008)","OEIS A000040: sequence of primes reference"]},"properties":{"applicability":"not-applicable","items":["primes below 100: 25 count","largest known prime digits: over 41 million digits - a Mersenne prime found in 2024"]},"recognition":{"applicability":"optional","items":["Divisible only by 1 and itself","Notation for special classes such as Mersenne primes 2^p - 1","Records such as the largest known prime","Numbers; notable primes are listed in tables and records."]},"capabilities":{"applicability":"required","items":["test primality","factor composite numbers into primes","search for large primes, such as Mersenne primes","use them, in cryptographic keys"]},"hazards":{"applicability":"required","items":["Using probable primes where proof is required","Weak primes in cryptography","Off-by-one errors in counting primes"]},"interfaces":{"applicability":"required","items":["FIPS 186 prime generation requirements for cryptography"]},"context":{"applicability":"required","items":["Primes are the building blocks of integers and underpin much of number theory and public-key cryptography.","Mersenne and double Mersenne primes","twin primes","palindromic primes","titanic and gigantic primes by size","provable versus probable primes"]}},"sources":[{"title":"Wikidata item Q49008: prime number","url":"https://www.wikidata.org/wiki/Q49008","note":"identity and sense of the item"},{"title":"Wikipedia: Prime number","url":"https://en.wikipedia.org/wiki/Prime_number","note":"general description of the item"}],"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?"],"resources":{"spec":"/models/things/publications/thing-q49008/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q49008/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-11T05:41:46Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-06T19:52:00+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}