{
  "prefix": {
    "pe": "https://proofengine.info/proofs/2026-being-divisible-by-2-3-7-11-13-17-proves-it-h/",
    "prov": "http://www.w3.org/ns/prov#",
    "xsd": "http://www.w3.org/2001/XMLSchema#",
    "schema": "http://schema.org/"
  },
  "entity": {
    "pe:claim": {
      "prov:type": "pe:Claim",
      "prov:label": "2026 being divisible by 2, 3, 7, 11, 13, 17 proves it has \"hidden perfect number properties.\"",
      "prov:value": "2026 being divisible by 2, 3, 7, 11, 13, 17 proves it has \"hidden perfect number properties.\""
    },
    "pe:evidence-A1": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "2026 divisible by 2: 2026 % 2 == 0",
      "pe:factId": "A1",
      "pe:evidenceType": "computed",
      "pe:method": "2026 % 2",
      "pe:result": "remainder=0, divisible=True"
    },
    "pe:evidence-A2": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "2026 divisible by 3: 2026 % 3 == 0",
      "pe:factId": "A2",
      "pe:evidenceType": "computed",
      "pe:method": "2026 % 3",
      "pe:result": "remainder=1, divisible=False"
    },
    "pe:evidence-A3": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "2026 divisible by 7: 2026 % 7 == 0",
      "pe:factId": "A3",
      "pe:evidenceType": "computed",
      "pe:method": "2026 % 7",
      "pe:result": "remainder=3, divisible=False"
    },
    "pe:evidence-A4": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "2026 divisible by 11: 2026 % 11 == 0",
      "pe:factId": "A4",
      "pe:evidenceType": "computed",
      "pe:method": "2026 % 11",
      "pe:result": "remainder=2, divisible=False"
    },
    "pe:evidence-A5": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "2026 divisible by 13: 2026 % 13 == 0",
      "pe:factId": "A5",
      "pe:evidenceType": "computed",
      "pe:method": "2026 % 13",
      "pe:result": "remainder=11, divisible=False"
    },
    "pe:evidence-A6": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "2026 divisible by 17: 2026 % 17 == 0",
      "pe:factId": "A6",
      "pe:evidenceType": "computed",
      "pe:method": "2026 % 17",
      "pe:result": "remainder=3, divisible=False"
    },
    "pe:evidence-A7": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "Prime factorization of 2026 (trial division)",
      "pe:factId": "A7",
      "pe:evidenceType": "computed",
      "pe:method": "Trial division prime factorization",
      "pe:result": "2 \u00d7 1013"
    },
    "pe:evidence-A8": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "SC2 check: sum of proper divisors of 2026 vs 2026 (perfect number test)",
      "pe:factId": "A8",
      "pe:evidenceType": "computed",
      "pe:method": "Sum of proper divisors via trial division",
      "pe:result": "sigma_proper(2026)=1016, required=2026, difference=-1010, classification=deficient"
    },
    "pe:evidence-A9": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "Cross-check: divisibility via gcd(2026, d) == d for each claimed d",
      "pe:factId": "A9",
      "pe:evidenceType": "computed",
      "pe:method": "gcd(2026, d) == d for each d in {2,3,7,11,13,17}",
      "pe:result": "GCD method: 1/6 divisibilities hold, agrees with modulo method (1/6)"
    },
    "pe:verdict": {
      "prov:type": "pe:Verdict",
      "prov:label": "Verdict: DISPROVED",
      "prov:value": "DISPROVED"
    }
  },
  "activity": {
    "pe:determine-verdict": {
      "prov:type": "pe:VerdictDetermination",
      "prov:label": "Determine verdict from evidence",
      "prov:endTime": "2026-03-28"
    }
  },
  "agent": {
    "pe:proof-engine": {
      "prov:type": "prov:SoftwareAgent",
      "prov:label": "Proof Engine",
      "schema:version": "0.10.0",
      "schema:url": "https://github.com/yaniv-golan/proof-engine"
    }
  },
  "wasGeneratedBy": {
    "pe:gen-verdict": {
      "prov:entity": "pe:verdict",
      "prov:activity": "pe:determine-verdict"
    }
  },
  "wasDerivedFrom": {},
  "wasAttributedTo": {
    "pe:attr-verdict": {
      "prov:entity": "pe:verdict",
      "prov:agent": "pe:proof-engine"
    }
  },
  "used": {
    "pe:used-A1": {
      "prov:activity": "pe:determine-verdict",
      "prov:entity": "pe:evidence-A1"
    },
    "pe:used-A2": {
      "prov:activity": "pe:determine-verdict",
      "prov:entity": "pe:evidence-A2"
    },
    "pe:used-A3": {
      "prov:activity": "pe:determine-verdict",
      "prov:entity": "pe:evidence-A3"
    },
    "pe:used-A4": {
      "prov:activity": "pe:determine-verdict",
      "prov:entity": "pe:evidence-A4"
    },
    "pe:used-A5": {
      "prov:activity": "pe:determine-verdict",
      "prov:entity": "pe:evidence-A5"
    },
    "pe:used-A6": {
      "prov:activity": "pe:determine-verdict",
      "prov:entity": "pe:evidence-A6"
    },
    "pe:used-A7": {
      "prov:activity": "pe:determine-verdict",
      "prov:entity": "pe:evidence-A7"
    },
    "pe:used-A8": {
      "prov:activity": "pe:determine-verdict",
      "prov:entity": "pe:evidence-A8"
    },
    "pe:used-A9": {
      "prov:activity": "pe:determine-verdict",
      "prov:entity": "pe:evidence-A9"
    }
  }
}