Source: https://guthlabs.ai/docs/instruments/primality-tester/implementation/

instrument implementation / implementation-contract

# Primality Tester implementation

A source-bound implementation contract for Primality Tester; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t4-124

**Effect**: Computation or source lookup only

## Input and validation requirements

The mathematical checks have clear expected behavior, but the specification leaves the Miller-Rabin/trial-division cutover and negative-integer convention unspecified. An implementation could route boundary-sized values inconsistently, return an undefined result for negative inputs, or silently test the absolute value of a negative input.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "n": "29",
    "method": "trial_division"
  },
  "expected_outputs": {
    "verdict": "prime",
    "confidence": "exact (100%)",
    "small_factors": []
  },
  "working": "floor(sqrt(29)) = 5 because 5^2 = 25 and 6^2 = 36. Test divisors 2, 3, and 5: 29 mod 2 = 1, 29 mod 3 = 2, and 29 mod 5 = 4. No divisor is found through 5, so 29 is prime. Factor list = []."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/primality-tester/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/primality-tester/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/primality-tester/qualification/>)

## 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`