{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.almost-prime","code":"thing-q936614","url":"https://ver.cy/models/thing/q936614/","name":"almost prime","alternateNames":[],"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":"A positive integer with exactly k prime factors counted with multiplicity, called a k-almost prime, so that primes are 1-almost primes, semiprimes such as 6, 9 and 15 are 2-almost primes, and numbers such as 8, 12 and 18 are 3-almost primes; almost primes are studied in analytic number theory, where sieve methods prove results about them that approach results about primes, as in Chen's theorem that every sufficiently large even integer is the sum of a prime and a number with at most two prime factors counted with multiplicity.","purpose":"Let an agent define almost primes and their classes, give examples, relay their role in sieve theory and results such as Chen theorem, and help classify a number by its count of prime factors.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Counts factors with multiplicity","Primes as the k equals 1 case","Sieve theory tool","Chen theorem"],"structure":{"bundles":[{"id":"define","name":"Define","description":"What almost primes are.","layers":[{"id":"definition","name":"Definition","description":"Definition and classes.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What is a k-almost prime, and what are the first members of each class?","kind":"definition"},{"text":"Is the number classified by factors with or without 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there up to x, asymptotically?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]}]},{"id":"theory","name":"Theory","description":"Sieve theory.","layers":[{"id":"sieves","name":"Sieves","description":"Sieve methods.","findings":[{"id":"sieves-finding","name":"Sieves","description":"Sieves.","questions":[{"text":"How do sieve methods yield results about almost primes?","kind":"provenance"},{"text":"Which entry fits sieve theory?","kind":"action"}]}]},{"id":"chen","name":"Chen","description":"Chen theorem.","findings":[{"id":"chen-finding","name":"Chen","description":"Chen.","questions":[{"text":"What does Chen theorem say, and how does it relate to the Goldbach conjecture?","kind":"provenance"},{"text":"Which entry fits Chen theorem?","kind":"action"}]}]}]},{"id":"context","name":"Context","description":"Applications and history.","layers":[{"id":"applications","name":"Applications","description":"Applications.","findings":[{"id":"applications-finding","name":"Applications","description":"Applications.","questions":[{"text":"Where do semiprimes and almost primes appear in cryptography and elsewhere?","kind":"provenance"},{"text":"Which entry fits RSA?","kind":"action"}]}]},{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did the study of almost primes develop in twentieth-century number theory?","kind":"provenance"},{"text":"Which sources are cited?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Define k-almost primes and check whether a number is one, showing factorisation.","Explain related results with sources."],"mustNot":["Forget multiplicity when counting prime factors.","Confuse almost primes with squarefree numbers.","Overstate results as statements about primes.","Report unverified computations as confirmed."],"requiresHuman":["Publishing new claimed results."]},"ethics":{"considerations":["Accurate definitions matter for students.","Correct credit for results matters to mathematicians."],"affectedParties":["Students","Mathematicians"]},"owners":{"steward":"Nobody: a mathematical concept held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q16317911","type":"parent","note":"registry parent class"},{"target":"positive integer","type":"related","note":"in registry terms"},{"target":"semiprime","type":"related","note":"the case k equals 2"},{"target":"prime number","type":"related","note":"the case k equals 1"},{"target":"sieve theory","type":"related","note":"in analytic number theory"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.almost-prime","Wikidata: Q936614 (https://www.wikidata.org/wiki/Q936614)","OEIS: A001358 for semiprimes, A014612 for 3-almost primes"]},"properties":{"applicability":"not-applicable","items":["2-almost primes: 4, 6, 9, 10, 14, 15, 21, 22 sequence - semiprimes","3-almost primes: 8, 12, 18, 20, 27, 28, 30 sequence"]},"recognition":{"applicability":"optional","items":["Exactly k prime factors with multiplicity","Primes, semiprimes and higher classes","Squarefree numbers and composite numbers are different classifications","Not a visible object; integers classified by factor count."]},"capabilities":{"applicability":"required","items":["define k-almost primes","give examples and counts","relay sieve theory results","classify numbers"]},"hazards":{"applicability":"required","items":["Forgetting multiplicity in counting factors","Confusing almost primes with squarefree numbers","Overstating results as statements about primes"]},"interfaces":{"applicability":"required","items":["No regulation; the OEIS is the reference database"]},"context":{"applicability":"required","items":["A concept in number theory and sieve methods.","1-almost primes, the primes","2-almost primes, the semiprimes","3-almost primes and higher classes","almost primes in arithmetic progressions","almost prime values of polynomials"]}},"sources":[{"title":"Wikidata item Q936614: almost prime","url":"https://www.wikidata.org/wiki/Q936614","note":"identity and sense of the item"},{"title":"Wikipedia: Almost prime","url":"https://en.wikipedia.org/wiki/Almost_prime","note":"general description of the item"}],"openQuestions":["Should semiprime be a separate primary entry?","How should the OEIS be linked?","How should sieve theory results be recorded?"],"resources":{"spec":"/models/things/publications/thing-q936614/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q936614/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T23:55:53Z","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 2026-10-07T10:10:33+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}}