{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.thabit-number","code":"thing-q965294","url":"https://ver.cy/models/thing/q965294/","name":"Thabit 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":"An integer of the form 3 times 2 to the n minus 1 for a non-negative integer n, the sequence beginning 2, 5, 11, 23, 47, 95, 191, named after the ninth-century mathematician Thabit ibn Qurra, who used them in his rule for generating amicable numbers; Thabit primes are those that are prime, such as 2, 5, 11, 23, 47, 191, 383 and 6143, and are searched for in distributed computing projects.","purpose":"Let an agent define Thabit numbers and Thabit primes, relay their role in Thabit rule for amicable numbers, relay known results and searches, and distinguish them from related forms such as Proth and Mersenne numbers.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Simple closed form","Amicable number link","Ninth-century origin","Search target"],"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 Thabit number, and how does it relate to Mersenne and Proth numbers?","kind":"definition"},{"text":"Is the question about Thabit, Mersenne or Proth numbers?","kind":"boundary"}]}]},{"id":"sequence","name":"Sequence","description":"Sequence.","findings":[{"id":"sequence-finding","name":"Sequence","description":"Sequence.","questions":[{"text":"What are the first Thabit numbers and primes, and where are they catalogued?","kind":"measurement"},{"text":"Which entry fits Proth number?","kind":"action"}]}]}]},{"id":"amicable","name":"Amicable","description":"Amicable numbers.","layers":[{"id":"rule","name":"Rule","description":"Thabit rule.","findings":[{"id":"rule-finding","name":"Rule","description":"Rule.","questions":[{"text":"How does Thabit rule use these numbers to generate amicable pairs?","kind":"provenance"},{"text":"Which entry fits amicable number?","kind":"action"}]}]},{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did Thabit ibn Qurra, Fermat, Descartes and Euler develop the rule?","kind":"provenance"},{"text":"Which sources are cited?","kind":"provenance"}]}]}]},{"id":"primes","name":"Primes","description":"Thabit primes.","layers":[{"id":"results","name":"Results","description":"Known results.","findings":[{"id":"results-finding","name":"Results","description":"Results.","questions":[{"text":"What is known about Thabit primes, including divisibility results?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]},{"id":"searches","name":"Searches","description":"Searches.","findings":[{"id":"searches-finding","name":"Searches","description":"Searches.","questions":[{"text":"How are Thabit primes searched for in distributed projects, and what is the largest known?","kind":"provenance"},{"text":"Is the information current?","kind":"boundary"}]}]}]},{"id":"context","name":"Context","description":"Generalisations and use.","layers":[{"id":"generalised","name":"Generalised","description":"Generalisations.","findings":[{"id":"generalised-finding","name":"Generalised","description":"Generalised.","questions":[{"text":"What are Thabit numbers of the second kind and generalised forms?","kind":"provenance"},{"text":"Which entry fits generalised Thabit number?","kind":"action"}]}]},{"id":"education","name":"Education","description":"Teaching.","findings":[{"id":"education-finding","name":"Education","description":"Education.","questions":[{"text":"How can Thabit numbers be used to teach number theory and its history?","kind":"provenance"},{"text":"Which entry fits the history of mathematics in the Islamic world?","kind":"action"}]}]}]}]},"agentConduct":{"may":["Generate and test Thabit numbers and report which are prime, with the method used.","Explain their use by Thabit ibn Qurra for amicable numbers."],"mustNot":["Claim a large Thabit number is prime without a proof or a stated probable-prime test.","Credit the work of Thabit ibn Qurra to later mathematicians alone.","Confuse Thabit numbers with similar forms such as Proth or Mersenne numbers."],"requiresHuman":["Announcing a new Thabit prime as a record."]},"ethics":{"considerations":["Fair credit to medieval Islamic mathematics is part of an honest history of science.","Unverified record claims mislead the mathematical community."],"affectedParties":["Mathematicians","Students","Historians of science"]},"owners":{"steward":"The public: held in common as mathematical knowledge.","roles":[],"masterSystems":[]},"relations":[{"target":"Q28920052","type":"parent","note":"registry parent class"},{"target":"non-negative integer","type":"related","note":"in registry terms"},{"target":"Thabit ibn Qurra","type":"related","note":"the mathematician"},{"target":"Thabit rule for amicable numbers","type":"related","note":"the classical construction"},{"target":"OEIS","type":"related","note":"as A055010"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.thabit-number","Wikidata: Q965294 (https://www.wikidata.org/wiki/Q965294)","OEIS: A055010 Thabit numbers","OEIS: A007505 Thabit primes"]},"properties":{"applicability":"not-applicable","items":["first Thabit prime: 2 number - n equals 0","known Thabit primes: over 60 count - as of recent searches"]},"recognition":{"applicability":"optional","items":["Numbers 3 times 2^n minus 1","Sequence OEIS A055010, Thabit primes A007505","Mersenne numbers are 2^n minus 1; Proth numbers are k times 2^n plus 1","The sequence 2, 5, 11, 23, 47, 95, 191, 383, ..."]},"capabilities":{"applicability":"required","items":["define and list","explain the amicable number rule","relay primes and searches","distinguish related forms"]},"hazards":{"applicability":"required","items":["Confusing with Mersenne or Proth numbers","Stale lists of known primes","Computation errors"]},"interfaces":{"applicability":"required","items":["No regulation; mathematical conventions"]},"context":{"applicability":"required","items":["Not applicable; a class of integers.","Thabit numbers in general","Thabit primes","Thabit numbers of the second kind, 3 times 2^n plus 1","generalised Thabit numbers in other bases"]}},"sources":[{"title":"Wikidata item Q965294: Thabit number","url":"https://www.wikidata.org/wiki/Q965294","note":"identity and sense of the item"},{"title":"Wikipedia: Thabit number","url":"https://en.wikipedia.org/wiki/Thabit_number","note":"general description of the item"}],"openQuestions":["Are there infinitely many Thabit primes?","How should OEIS and search projects be linked?","How should the amicable number rule be recorded?"],"resources":{"spec":"/models/things/publications/thing-q965294/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q965294/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 2026-10-06T19:52:03+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}}