Prime Checker & Generator (Sieve) mechanism

Model scope

The named algorithms are standard, but the specification is incomplete for a deterministic, testable instrument contract. Exact Miller-Rabin bases/rounds, range endpoint semantics, nth-prime indexing, twin-prime output semantics, integer-size limits, and invalid-input behavior must be defined before approval.

• Miller-Rabin is a valid probabilistic primality algorithm, but the spec does not define the witness-base selection, number of rounds, failure probability, or behavior for small n.
• The sieve formula is named but not fully specified: the implementation must mark composites using prime factors up to floor(sqrt(maximum range endpoint)) and define whether endpoints are included.
• No formula or algorithm is specified for nth-prime generation; indexing is ambiguous because nth prime could be 0-based or 1-based.
• No formula or algorithm is specified for twin-prime finding, including whether the output is pairs, individual primes, or only a boolean and how range boundaries are handled.
• The honest label correctly states that Miller-Rabin is probabilistic for sufficiently large numbers, but it should also identify any deterministic numeric range or the selected bases and error bound.

Units and conventions

• Inputs are mathematical integers, dimensionless; non-integers and non-finite values must be rejected.
• For these vectors, a range [a,b] is assumed to be inclusive at both endpoints; the spec does not state whether ranges are inclusive or exclusive.
• For these vectors, nth-prime indexing is assumed to be 1-based, so the 1st prime is 2; the spec does not state the indexing convention.
• For JavaScript numeric inputs, exact integer representation is assumed only through 2^53-1 unless arbitrary-precision integers are used; this constraint is not stated.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "operation": "primality_test",
    "n": 1
  },
  "expected_outputs": {
    "prime": false,
    "classification": "composite"
  },
  "working": "1 is less than 2. By definition, primes are integers greater than 1. Therefore 1 is not prime and the result is composite/non-prime."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The extreme integer 9007199254740993 cannot be represented exactly by ordinary JavaScript Number arithmetic and silently rounds to 9007199254740992. Accepting it without rejection or exact-integer handling can invalidate primality and range results. The range endpoint convention is also ambiguous unless explicitly defined.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json