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    "Trial division",
    "n = 1 is neither prime nor composite"
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    "Trial division only — not a primality-proving sieve for cryptographic sizes",
    "n = 1 is neither prime nor composite (empty factorization)",
    "Domain 1 ≤ n ≤ 10^12",
    "n < 1 → VALUE_MUST_BE_POSITIVE",
    "unknown mode → INVALID_MODE"
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  "boundary_conditions": [
    "missing n → MISSING_REQUIRED_INPUT",
    "n < 1 → VALUE_MUST_BE_POSITIVE",
    "n > 10^12 → VALUE_ABOVE_MAX",
    "unknown mode → INVALID_MODE"
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  "sources": [
    "ISO 80000-2:2019 Quantities and units — Mathematics (primes / factorization)",
    "Fundamental theorem of arithmetic"
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        "canonical": "13"
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        "mode": "factorize",
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        "factors": [
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            "e": 1
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        "omega": 1,
        "big_omega": 1,
        "max_n": 1000000000000
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      "tol": null
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        "n": 1
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        "omega": 0
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