{"query": "The integers, examined: a prime, a divisor, a factorial", "count": 20, "results": [{"id": "card_works_number_theory", "title": "The integers, examined: a prime, a divisor, a factorial", "shelf": "the-works", "surface": "secular", "snippet": "Exact facts about whole numbers, decided by algorithm, not by eye: 97 is prime; 48 and 36 share a greatest common divisor of 12; and 6! counts the orderings of six things.  Worked & sealed by the engi", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_src_openstax_contemporary_mathematics_key_terms_746b90b5", "title": "Key Terms — Contemporary Mathematics", "shelf": "reference", "surface": "secular", "snippet": "Key Terms\n\n3.1\n\nPrime and Composite Numbers\n\nnatural numbers\n\nfactor of a number\n\nmultiple of a number\n\nprime number\n\ncomposite number\n\nprime factorization\n\ngreatest common divisor (GCD)\n\nleast common", "authority_tier": "reference", "source": "OpenStax: Contemporary Mathematics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_chain_deligne_1971", "title": "Deligne 1971 — Théorie de Hodge, II", "shelf": "codex", "surface": "secular", "snippet": "P. Deligne (1971). Théorie de Hodge, II. Publ. Math. IHÉS 40 (1971) 5–57. DOI 10.1007/BF02684692. Canonical: https://doi.org/10.1007/BF02684692. Free copy: http://www.numdam.org/item/PMIHES_1971__40__", "authority_tier": "reference", "source": "P. Deligne (1971), Publ. Math. IHÉS 40 (1971) 5–57", "readable": false, "generated": false}, {"id": "card_src_openstax_contemporary_mathematics_key_concepts_7ea7697d", "title": "Key Concepts — Contemporary Mathematics", "shelf": "reference", "surface": "secular", "snippet": "Key Concepts\n\n3.1\n\nPrime and Composite Numbers\n\nThe natural numbers can be categorized as 1, prime numbers, and composite numbers.\n\nPrime numbers have as their only factors 1 and themselves.\n\nComposit", "authority_tier": "reference", "source": "OpenStax: Contemporary Mathematics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_chain_lefschetz_1924", "title": "Lefschetz 1924 — L'analysis situs et la géométrie algébrique", "shelf": "codex", "surface": "secular", "snippet": "S. Lefschetz (1924). L'analysis situs et la géométrie algébrique. Gauthier-Villars, Paris, 1924. Cited by its record. License as found: public domain (the author died more than a century ago, or the w", "authority_tier": "reference", "source": "S. Lefschetz (1924), Gauthier-Villars, Paris, 1924", "readable": false, "generated": false}, {"id": "card_src_openstax_contemporary_mathematics_3_1_prime_and_composite_numbers_00cf5abc", "title": "3.1 Prime and Composite Numbers — Contemporary Mathematics", "shelf": "reference", "surface": "secular", "snippet": "3.1\n\nPrime and Composite Numbers\n\nFigure\n3.2\n\nComputers are protected using encryption based on prime numbers. (credit: “Data Security” by Blogtrepreneur/Flickr, CC BY 2.0)\n\nAfter completing this sect", "authority_tier": "reference", "source": "OpenStax: Contemporary Mathematics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_alm_connection_euclid_euler_perfect_numbers", "title": "Almanac: Euclid-Euler: every even perfect number is a Mersenne prime times a power of two", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  A perfect number equals the sum of its own proper divisors -- 6 = 1+2+3, 28 = 1+2+4+7+14 -- and Euclid (Book IX) plus Euler proved exactly where they come from: every even perfect number i", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_src_openstax_contemporary_mathematics_chapter_review_fcae2325", "title": "Chapter Review — Contemporary Mathematics", "shelf": "reference", "surface": "secular", "snippet": "Chapter Review\n\nPrime and Composite Numbers\n\n1\n.\n\nIdentify which of the following numbers are prime, composite, or neither:\n\n201, 34, 17, 1, 37.\n\n2\n.\n\nFind the prime factorization of 500.\n\n3\n.\n\nFind t", "authority_tier": "reference", "source": "OpenStax: Contemporary Mathematics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_word_divisor", "title": "divisor", "shelf": "dictionary", "surface": "secular", "snippet": "divisor: (noun) one of two or more integers that can be exactly divided into another integer — syn: factor · (noun) the number by which a dividend is divided", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_word_greatest_common_divisor", "title": "greatest common divisor", "shelf": "dictionary", "surface": "secular", "snippet": "greatest common divisor: (noun) the largest integer that divides without remainder into a set of integers — syn: greatest common factor, highest common factor", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_word_prime_quantity", "title": "prime quantity", "shelf": "dictionary", "surface": "secular", "snippet": "prime quantity: (noun) a natural number that has exactly two distinct natural number divisors: 1 and itself — syn: prime", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_word_prime", "title": "prime", "shelf": "dictionary", "surface": "secular", "snippet": "prime: (noun) a natural number that has exactly two distinct natural number divisors: 1 and itself — syn: prime quantity · (noun) the period of greatest prosperity or productivity — syn: flower, peak,", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_etym_divisor", "title": "divisor", "shelf": "etymology", "surface": "secular", "snippet": "divisor: etymology (Webster 1913) — n.: [L., fr. dividere. See Divide.]. From Webster's Revised Unabridged Dictionary (1913), public domain.", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_seal_f0ae09e9e181922d6a5d5edef35f2cd4755e15b7fa17a2531bc8f292c43e6909", "title": "Receipt f0ae09e9e181… — sealed: candidate_set", "shelf": "seals", "surface": "secular", "snippet": "{\n \"candidate_set_id\": \"cset_6ba6dac164ceae53190b30d19f6106d9\",\n \"candidates\": [\n  {\n   \"candidate_id\": \"c000\",\n   \"cluster_id\": null,\n   \"evidence\": {\n    \"checked_by\": \"concordance.derivation.verify", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_src_pron_divisor", "title": "divisor", "shelf": "pronunciation", "surface": "secular", "snippet": "divisor: pronounced (ARPABET) D IH0 V AY1 Z ER0. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "readable": false, "generated": false}, {"id": "card_v_e4e8d2f7bc61", "title": "10 has 6 divisors", "shelf": "number_theory", "surface": "secular", "snippet": "Verdict: BROKEN.\n• number_theory.divisor_count: 10 has 4 divisors, not 6\nSealed and independently re-checkable: https://narrowhighway.org/s/97c6e9e4a144d17c349d91887338c6d3112b81c996acda07e18591dad2ab", "authority_tier": "engine", "source": "Verified by the engine — number_theory", "readable": false, "generated": false}, {"id": "card_v_c6bb53eebbde", "title": "60 has twelve divisors", "shelf": "number_theory", "surface": "secular", "snippet": "Verdict: HOLDS.\n• number_theory.divisor_count: 60 has 12 divisors: [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]\nSealed and independently re-checkable: https://narrowhighway.org/s/29d155e0711a28a6e27dd32", "authority_tier": "engine", "source": "Verified by the engine — number_theory", "readable": false, "generated": false}, {"id": "card_v_d669a05e5720", "title": "the number of divisors of 12 is 6", "shelf": "number_theory", "surface": "secular", "snippet": "Verdict: HOLDS.\n• number_theory.divisor_count: 12 has 6 divisors: [1, 2, 3, 4, 6, 12]\nSealed and independently re-checkable: https://narrowhighway.org/s/dc49a47fb420feba491cfd9fe3e0b0a3cfe908d9deaf50d", "authority_tier": "engine", "source": "Verified by the engine — number_theory", "readable": false, "generated": false}, {"id": "card_src_word_aliquot", "title": "aliquot", "shelf": "dictionary", "surface": "secular", "snippet": "aliquot: (noun) an integer that is an exact divisor of some quantity — syn: aliquot part · (adjective) signifying an exact divisor or factor of a quantity", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_seal_97c6e9e4a144d17c349d91887338c6d3112b81c996acda07e18591dad2abb7f8", "title": "Receipt 97c6e9e4a144… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"number_theory\",\n  \"dimensions\": [\n   \"discreteness\",\n   \"reasoning\"\n  ]\n },\n \"gate_results\": [\n  {\n   \"details\": {\n    \"broken_at\": \"a1\",\n    \"confirmed_", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_works_number_theory"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}