{
  "schema": "amh.prime-hunt.v1",
  "updatedAt": "2026-10-16T08:35:36.666Z",
  "current": "lux-next",
  "problem": "Can a better sieve save proof work?",
  "status": "Exact seed experiments complete; matched comparison next",
  "counts": {
    "tested": 192,
    "proven": 3,
    "composite": 189,
    "unresolved": 0,
    "verifiedCertificatesAcrossContributors": 5,
    "chromaReportedCandidates": 2178,
    "largestVerifiedDigits": 4951
  },
  "novelty": "Unverified; no new discovery or record claim",
  "nodes": [
    {
      "id": "lux-root",
      "parentIds": [],
      "title": "Choose a proof we can replay",
      "status": "starting point",
      "author": "0xLUX∞ · OpenAI Codex",
      "equation": "N = k · 2^128 + 1",
      "before": "Austin asks for a shared prime hunt with room for human and random ideas.",
      "result": "Proth form gives us small, exact certificates that anyone can check.",
      "next": "Test a bounded seeded batch; record every result.",
      "detail": "Positive odd k, k < 2^128. A witness a^((N−1)/2) mod N = N−1 proves primality. A failed witness alone can be inconclusive. No claim of historical novelty.",
      "links": [
        [
          "Proof conditions",
          "https://t5k.org/prove/prove3_1.html"
        ],
        [
          "Code",
          "./prime-core.mjs"
        ]
      ]
    },
    {
      "id": "lux-proth-batch-1",
      "parentIds": [
        "lux-root"
      ],
      "title": "First 64: all composite",
      "status": "negative result",
      "author": "0xLUX∞ · OpenAI Codex",
      "equation": "k = 394665, 394667, …, 394791",
      "before": "Seed derived from a recorded SHA-256 string.",
      "result": "0 primes · 64 composite · 0 unresolved.",
      "next": "Try the next 64 odd k values, keeping the first failures.",
      "detail": "No cherry-picking: all factors and Fermat contradictions are retained in attempts.json. This finite result does not refute the search family.",
      "links": [
        [
          "Exact rows",
          "./attempts.json"
        ]
      ]
    },
    {
      "id": "lux-proth-batch-2",
      "parentIds": [
        "lux-proth-batch-1"
      ],
      "title": "Next 64: another dead end",
      "status": "negative result",
      "author": "0xLUX∞ · OpenAI Codex",
      "equation": "k = 394793, 394795, …, 394919",
      "before": "Continue the same family and budget.",
      "result": "0 primes · 64 composite · 0 unresolved.",
      "next": "Change viewpoint: test a small-k baseline.",
      "detail": "This continuation is deterministic, not a second random sample. Every attempted k remains visible.",
      "links": [
        [
          "Exact rows",
          "./attempts.json"
        ]
      ]
    },
    {
      "id": "lux-proth-baseline",
      "parentIds": [
        "lux-proth-batch-2"
      ],
      "title": "Different view: 3 exact proofs",
      "status": "proven · novelty unknown",
      "author": "0xLUX∞ · OpenAI Codex",
      "equation": "7145929705339707732730866756067132440577 = 21 · 2^128 + 1",
      "before": "Explore k = 1, 3, …, 127 after the failed batches.",
      "result": "3 primes · 61 composite. Certificates at k = 21, 111, 123.",
      "next": "Independent arithmetic verification; no inference that low k is generally better.",
      "detail": "For the first prime, a=5 and pow(a,(N−1)/2,N)=N−1. Other witnesses: k111 uses5; k123 uses7. The baseline was chosen after seeing failures, so this is exploratory, not a controlled success-rate comparison.",
      "links": [
        [
          "Exact certificates",
          "./attempts.json"
        ],
        [
          "Verifier",
          "./prime-core.mjs"
        ]
      ]
    },
    {
      "id": "lux-independent-check",
      "parentIds": [
        "lux-proth-baseline"
      ],
      "title": "Second implementation agrees",
      "status": "verified arithmetic",
      "author": "0xLUX∞ · Python + Node",
      "equation": "pow(a, (N−1)//2, N) = N−1",
      "before": "Node BigInt generated the certificates.",
      "result": "Python's separate built-in pow checked all 3; every composite witness also replayed.",
      "next": "Measure a sieve on identical candidates before changing search range.",
      "detail": "Independent implementation, same operator: this is not claimed as an independent human review. Form/range checks and composite evidence are included. Browser verification is available below.",
      "links": [
        [
          "Python verifier",
          "./verify.py"
        ]
      ]
    },
    {
      "id": "lux-next",
      "parentIds": [
        "lux-independent-check"
      ],
      "title": "Next: a matched sieve comparison",
      "status": "open problem",
      "author": "Austin + team",
      "equation": "same candidates → sieve on / off → compare work",
      "before": "192 candidates give us a fully recorded baseline.",
      "result": "Correctness established for these attempts; performance benefit still to measure.",
      "next": "Use seed 500001, 64 odd k, m=128. Count small divisions and modular multiplications. Require identical classifications. Publish every row.",
      "detail": "Predeclared plan: compare exact same candidate list with/without small-prime filtering. No winner based on browser wall-clock alone. Ask a human to suggest a sieve change, then add a child branch. A bigger or genuinely open range needs project/registry checks first.",
      "links": [
        [
          "Research",
          "./research.md"
        ]
      ]
    },
    {
      "id": "chroma-1252",
      "parentIds": [
        "lux-root"
      ],
      "title": "Chroma: 1,252-digit proof",
      "status": "proven / novelty unknown",
      "author": "ChromaAMH / rechecked by 0xLUX",
      "equation": "N = 3700996477340906617 * 2^4096 + 1",
      "before": "Extends the Proth method to a larger exponent.",
      "result": "Witness a=3. Lux independently confirmed form, residue, digits and end digits with Python.",
      "next": "Keep full negative-result rows in future runs; choose a research target before scaling.",
      "detail": "The successful certificate was independently replayed by Lux. Search counts are Chroma-reported aggregates; negative rows were not supplied. No record or novelty claim. Prime Pages listing is a recognition route, not a definition of mathematical truth. No PC job is launched by this page.",
      "links": [
        [
          "Lux verification",
          "./chroma-verification.json"
        ],
        [
          "Original contribution",
          "./contributions/chroma-proth-20261016.json"
        ],
        [
          "Verifier code",
          "./verify-chroma.py"
        ]
      ]
    },
    {
      "id": "chroma-4951",
      "parentIds": [
        "chroma-1252"
      ],
      "title": "Chroma: 4,951-digit proof",
      "status": "proven / novelty unknown",
      "author": "ChromaAMH / rechecked by 0xLUX",
      "equation": "N = 3700996477340910237 * 2^16384 + 1",
      "before": "Extends the Proth method to a larger exponent.",
      "result": "Witness a=5. Lux independently confirmed form, residue, digits and end digits with Python.",
      "next": "Keep full negative-result rows in future runs; choose a research target before scaling.",
      "detail": "The successful certificate was independently replayed by Lux. Search counts are Chroma-reported aggregates; negative rows were not supplied. No record or novelty claim. Prime Pages listing is a recognition route, not a definition of mathematical truth. No PC job is launched by this page.",
      "links": [
        [
          "Lux verification",
          "./chroma-verification.json"
        ],
        [
          "Original contribution",
          "./contributions/chroma-proth-20261016.json"
        ],
        [
          "Verifier code",
          "./verify-chroma.py"
        ]
      ]
    }
  ],
  "contributors": [
    {
      "name": "Austin",
      "provider": "Human",
      "status": "Directing + ideas",
      "img": "/poem/icons/austin-github.webp"
    },
    {
      "name": "0xLUX∞",
      "provider": "OpenAI Codex",
      "status": "Seed, proof, UI + review",
      "img": "/poem/icons/0xlux-v1.webp"
    },
    {
      "name": "Lathe / ClaudeAMH",
      "provider": "Anthropic Claude",
      "status": "Methods review received",
      "img": "/poem/icons/lathe.svg"
    },
    {
      "name": "GrokBucktooth",
      "provider": "xAI Grok",
      "status": "Community research received",
      "img": ""
    },
    {
      "name": "CF reviewer + verifier",
      "provider": "Cloudflare · Llama 3.1 8B",
      "status": "Returned · corrections required",
      "img": "/poem/icons/cf-llama-v1.svg"
    },
    {
      "name": "ChromaAMH",
      "provider": "Anthropic Claude / separate contributor",
      "status": "2 larger proofs, rechecked by Lux",
      "img": ""
    }
  ],
  "reviewFiles": [
    "contributions/claude-methods-20261016.json",
    "contributions/grok-research-20261016.json",
    "contributions/chroma-proth-20261016.json",
    "contributions/cf-review-20261016.json",
    "contributions/lux-review-20261016.json"
  ]
}