{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.lucky-number","code":"thing-q1428157","url":"https://ver.cy/models/thing/q1428157/","name":"lucky number","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":"In number theory, a positive integer that survives a sieve similar to the sieve of Eratosthenes but based on position: starting from the odd numbers, every k-th remaining number is deleted where k is the next surviving number, leaving 1, 3, 7, 9, 13, 15, 21 and so on; the term is also used in popular culture for numbers people regard as fortunate, which is a different sense.","purpose":"Let an agent define lucky numbers in the mathematical sense, generate and test them, relate them to primes, and separate this sense from cultural beliefs about fortunate numbers, which are presented with attribution.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Defined by a sieve on positions, not divisibility","Shares distribution properties with primes","All lucky numbers are odd","Distinct from cultural lucky numbers"],"structure":{"bundles":[{"id":"define","name":"Define","description":"The sieve.","layers":[{"id":"sieve","name":"Sieve","description":"The procedure.","findings":[{"id":"sieve-finding","name":"Sieve","description":"Sieve.","questions":[{"text":"How does the lucky number sieve work, step by step?","kind":"definition"},{"text":"Is the question about the mathematical sense or about fortunate numbers in culture?","kind":"boundary"}]}]},{"id":"examples","name":"Examples","description":"First terms.","findings":[{"id":"examples-finding","name":"Examples","description":"Examples.","questions":[{"text":"What are the lucky numbers below a given bound?","kind":"measurement"},{"text":"Which entry fits integer sequences?","kind":"action"}]}]}]},{"id":"properties","name":"Properties","description":"Known results.","layers":[{"id":"distribution","name":"Distribution","description":"Distribution.","findings":[{"id":"distribution-finding","name":"Distribution","description":"Distribution.","questions":[{"text":"How does the density of lucky numbers compare with primes, and what is proved versus conjectured?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]},{"id":"primes","name":"Lucky primes","description":"Lucky primes.","findings":[{"id":"primes-finding","name":"Primes","description":"Primes.","questions":[{"text":"Which numbers are both lucky and prime, and what is known about them?","kind":"provenance"},{"text":"Which entry fits prime numbers?","kind":"action"}]}]}]},{"id":"compute","name":"Compute","description":"Algorithms.","layers":[{"id":"algorithm","name":"Algorithm","description":"Generating.","findings":[{"id":"algorithm-finding","name":"Algorithm","description":"Algorithm.","questions":[{"text":"How is the sieve implemented efficiently, and how is membership tested?","kind":"action"},{"text":"What are the complexity and limits?","kind":"measurement"}]}]},{"id":"variants","name":"Variants","description":"Variants.","findings":[{"id":"variants-finding","name":"Variants","description":"Variants.","questions":[{"text":"What variants of the sieve exist, and how do they relate?","kind":"provenance"},{"text":"Should a variant be a separate entry?","kind":"boundary"}]}]}]},{"id":"context","name":"Context","description":"History and culture.","layers":[{"id":"history","name":"History","description":"Origin.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did Ulam and colleagues introduce lucky numbers, and why the name?","kind":"provenance"},{"text":"Which entry fits Stanislaw Ulam?","kind":"action"}]}]},{"id":"culture","name":"Culture","description":"Cultural sense.","findings":[{"id":"culture-finding","name":"Culture","description":"Culture.","questions":[{"text":"How do cultures regard certain numbers as lucky, presented with attribution and without endorsement?","kind":"provenance"},{"text":"Is the presentation neutral?","kind":"boundary"}]}]}]}]},"agentConduct":{"may":["Explain the lucky number sieve and compute lucky numbers.","Compare their properties with primes, with sources."],"mustNot":["Confuse sieve lucky numbers with numbers considered lucky by superstition.","Present unproven conjectures about them as theorems.","Use the term to promote gambling or numerology."],"requiresHuman":["Publishing new results about them."]},"ethics":{"considerations":["Confusion with luck can support gambling and superstition.","Rigorous treatment matters for students learning number theory."],"affectedParties":["Students","People prone to gambling"]},"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":"a property of integers"},{"target":"prime number","type":"related","note":"similar distribution"},{"target":"On-Line Encyclopedia of Integer Sequences","type":"related","note":"sequence A000959"},{"target":"numerology","type":"related","note":"cultural beliefs about numbers"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.lucky-number","Wikidata: Q1428157 (https://www.wikidata.org/wiki/Q1428157)","OEIS: A000959 lucky numbers"]},"properties":{"applicability":"not-applicable","items":["first terms: 1, 3, 7, 9, 13, 15, 21 integers"]},"recognition":{"applicability":"optional","items":["Produced by the position-based sieve","Sequence 1, 3, 7, 9, 13, 15, 21, 25, 31","Culturally lucky numbers such as 7 or 8 are a different sense","Not visible; a property of integers."]},"capabilities":{"applicability":"required","items":["generate lucky numbers by the sieve","test whether an integer is lucky","compare their distribution with primes","distinguish the mathematical from the cultural sense"]},"hazards":{"applicability":"required","items":["Mixing the mathematical and cultural senses","Off-by-one errors in the sieve","Presenting conjectures as theorems"]},"interfaces":{"applicability":"required","items":["No regulation; definitions follow the literature and the OEIS"]},"context":{"applicability":"required","items":["Not for anything; an object of number theory.","lucky numbers of the Ulam sieve","lucky primes, which are both lucky and prime","variants of the sieve starting from other sets","cultural lucky numbers, a separate sense"]}},"sources":[{"title":"Wikidata item Q1428157: lucky number","url":"https://www.wikidata.org/wiki/Q1428157","note":"identity and sense of the item"},{"title":"Wikipedia: Lucky number","url":"https://en.wikipedia.org/wiki/Lucky_number","note":"general description of the item"}],"openQuestions":["Should the cultural sense be a separate entry?","How should OEIS entries be linked?","Which conjectures about lucky numbers should be recorded?"],"resources":{"spec":"/models/things/publications/thing-q1428157/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q1428157/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T19:51:39Z","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 2026-10-06T19:51:54+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}}