{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.probable-prime","code":"thing-q2654835","url":"https://ver.cy/models/thing/q2654835/","name":"probable prime","alternateNames":["industrial-grade prime"],"kind":"thing","status":"published","version":"0.2.0-wave.3","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QTY"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"An integer that satisfies a specified necessary condition for primality, such as a condition checked by a Fermat, Miller-Rabin or Baillie-PSW test, without thereby establishing a proof of primality. Composite numbers that satisfy such conditions are called pseudoprimes relative to the condition used. Passing a necessary condition alone does not establish a high likelihood of primality; confidence depends on the test, its assumptions and how candidates are selected. Probable primes, sometimes called industrial-grade primes, are used in cryptography where the required assurance does not demand a primality proof, and large probable primes such as certain Mersenne and repunit candidates are reported before proofs are available.","purpose":"Let an agent define probable primes and the tests that produce them, relay their use in cryptography and record searches, and distinguish probable primes from proven primes and pseudoprimes.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["A probable prime satisfies a specified necessary condition for primality.","The assurance provided depends on the test and its assumptions.","Probable-prime tests can offer fast screening.","Probable primes have cryptographic uses.","Passing a probable-prime test is distinct from proving primality."],"structure":{"bundles":[{"id":"define","name":"Define","description":"Definition.","layers":[{"id":"definition","name":"Definition","description":"Definition.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What is a probable prime, and how does it differ from a proven prime and a pseudoprime?","kind":"definition"},{"text":"Is the question about probable primes, proven primes or pseudoprimes?","kind":"boundary"}]}]},{"id":"tests","name":"Tests","description":"Tests.","findings":[{"id":"tests-finding","name":"Tests","description":"Tests.","questions":[{"text":"How do Fermat, Miller-Rabin and Baillie-PSW tests work, and what are their error bounds?","kind":"definition"},{"text":"Which entry fits the specific test?","kind":"action"}]}]}]},{"id":"use","name":"Use","description":"Use in practice.","layers":[{"id":"cryptography","name":"Cryptography","description":"Cryptography.","findings":[{"id":"cryptography-finding","name":"Cryptography","description":"Cryptography.","questions":[{"text":"How are probable primes generated for keys, and what do standards require?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]},{"id":"records","name":"Records","description":"Record searches.","findings":[{"id":"records-finding","name":"Records","description":"Records.","questions":[{"text":"What are the largest known probable primes, and how are they later proven?","kind":"provenance"},{"text":"Is the information current?","kind":"boundary"}]}]}]},{"id":"theory","name":"Theory","description":"Theory.","layers":[{"id":"pseudoprimes","name":"Pseudoprimes","description":"Pseudoprimes.","findings":[{"id":"pseudoprimes-finding","name":"Pseudoprimes","description":"Pseudoprimes.","questions":[{"text":"What pseudoprimes and Carmichael numbers defeat simple tests?","kind":"provenance"},{"text":"Which entry fits Carmichael number?","kind":"action"}]}]},{"id":"proof","name":"Proof","description":"Proving primality.","findings":[{"id":"proof-finding","name":"Proof","description":"Proof.","questions":[{"text":"How do deterministic tests such as AKS and ECPP prove primality?","kind":"provenance"},{"text":"Which sources are cited?","kind":"provenance"}]}]}]},{"id":"context","name":"Context","description":"History.","layers":[{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did probabilistic primality testing develop from Fermat to Rabin and beyond?","kind":"provenance"},{"text":"Which entry fits the history of computational number theory?","kind":"action"}]}]},{"id":"terminology","name":"Terminology","description":"Terminology.","findings":[{"id":"terminology-finding","name":"Terminology","description":"Terminology.","questions":[{"text":"Where does the term industrial-grade prime come from?","kind":"provenance"},{"text":"Which entry fits primality test?","kind":"action"}]}]}]}]},"agentConduct":{"may":["Run primality tests and report which tests were used, their assumptions and any applicable error bounds.","Mark a number as probable prime, not proven prime, until a proof is given."],"mustNot":["Present a probable prime as proven prime.","Use a test known to be fooled by pseudoprimes, such as a single Fermat base, for security keys.","Accept externally supplied primes for cryptography without independent testing.","Infer high confidence in primality merely from passing an arbitrary necessary condition."],"requiresHuman":["A human must approve prime generation methods for production cryptography."]},"ethics":{"considerations":["Weak primality checks have led to breakable cryptographic keys.","Mathematical records rely on honest distinction between probable and proven."],"affectedParties":["Users of cryptographic systems","Mathematicians","Software developers"]},"owners":{"steward":"The public: held in common as mathematical knowledge.","roles":[],"masterSystems":[]},"relations":[{"target":"Q16317911","type":"parent","note":"registry parent class"},{"target":"positive integer","type":"related","note":"in registry terms"},{"target":"primality test","type":"related","note":"such as Miller-Rabin"},{"target":"pseudoprime","type":"related","note":"a composite that passes"},{"target":"public-key cryptography","type":"related","note":"for key generation"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.probable-prime","Wikidata: Q2654835 (https://www.wikidata.org/wiki/Q2654835)"]},"properties":{"applicability":"not-applicable","items":["Miller-Rabin error bound: at most 1/4 per round - for composites"]},"recognition":{"applicability":"optional","items":["Integer passing probabilistic primality tests","Fermat, Miller-Rabin, Baillie-PSW probable primes","A proven prime has a certificate; a pseudoprime is a composite that passes","Not a visible object; a number with a test result."]},"capabilities":{"applicability":"required","items":["define and explain tests","relay use in cryptography","relay record searches","distinguish from proven primes"]},"hazards":{"applicability":"required","items":["Treating probable as proven","Insufficient test rounds","Adversarial composites against weak tests"]},"interfaces":{"applicability":"required","items":["FIPS 186 and other standards specifying probable prime generation","No regulation of the concept"]},"context":{"applicability":"required","items":["Efficient primality assurance in practice.","Fermat probable primes","strong or Miller-Rabin probable primes","Lucas and Baillie-PSW probable primes","industrial-grade primes in cryptography","large probable primes in record lists"]}},"sources":[{"title":"Wikidata item Q2654835: probable prime","url":"https://www.wikidata.org/wiki/Q2654835","note":"identity and sense of the item"},{"title":"Wikipedia: Probable prime","url":"https://en.wikipedia.org/wiki/Probable_prime","note":"general description of the item"}],"openQuestions":["Should Miller-Rabin and Baillie-PSW be the primary linked entries?","How should cryptographic standards be linked?","How should record probable primes be recorded?"],"resources":{"spec":"/models/things/publications/thing-q2654835/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q2654835/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-13T01:57:22Z","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 2026-10-07T10:10:29+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}}