math.prime_factorization

Three distinct suites: educational examples on the calculator page, this legacy regression count (11/11 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.0.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-28.meta-metrics-v2. Calculation version 1.0.1. CVP 1.0.0-proposed. 92/92 golden · 3/3 CVP boundary · 5/5 invalid · 3/3 property · 2/2 metamorphic · 3/3 cross-interface · 1/1 cross-calculator · 6/6 CVP contract. digest b9d3ea059680.

• Golden (oracle-backed) 92 / 92
• CVP boundary 3 / 3
• Invalid input 5 / 5
• Property 3 / 3
• Metamorphic 2 / 2
• Cross-interface 3 / 3
• Cross-calculator 1 / 1
• CVP contract 6 / 6
• Interfaces PASS · UI (SSR) / REST / MCP
• Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
• Verified scope Sampled complete packs for both published modes, one/prime/prime-powers/semiprimes and bounded near10^12 cases
• Assurance Core

• release artifacts aligned PASS
• schema output required declared PASS
• schema valid input executes PASS
• engine success output validates schema PASS
• schema rejects incomplete input PASS
• rest success payload validates schema PASS

Fingerprint sha256:b829da98c174e8e44f50bfa4a0125a9c3ce0f092ab89b9f50354ed9f72f90252

Input schema sha256:99609a1ee80f23d3800871c8cca1f0b5875203bf88dd49bc39bb4948e6833544 · Output schema sha256:b07a4605ef4dc94b608e7b0ffd20935d4b31e722999e7af449aaa8acad203955 · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Tool

prime-factorization

Engine

prime-factorization

Engine build

2026-10-23

Evidence core

2026-10-23T01:26:27.414Z

Rendered

2026-10-29T17:04:55.746Z

Last reviewed

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Assumptions

• Unique factorization (fundamental theorem of arithmetic)
• Trial division
• n = 1 is neither prime nor composite

Limitations

• 1<=n<=10^12; integer strings at most13 digits and512 characters, or safe JSON integers. Exactness starts at the normalized integer.
• n=1 has empty factors and is neither prime nor composite. Factors are sorted ascending; ω counts distinct primes and Ω counts multiplicity.
• Trial division bounded by sqrt(n); no floating convergence or cryptographic-size factorization service. Primality is a view of the complete factorization.
• Unknown keys, alias conflicts and invalid types reject. Share links execute the current engine. JSON numeric source follows the general binary64 transport policy; use digit strings for exact source input.