Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnly/idempotent/non-destructive, so the description's job is lighter; it adds genuinely new operational context: the input domain bound, a per-call price ($0.001 USDC via x402 on Solana), and an equivalent HTTPS endpoint. It does not state what the response looks like (a boolean), which is the only remaining gap.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The definition is front-loaded, examples earn their place by pinning down the square-factor exclusion, and the operational tail (range, price, URL) is compact. Four sentences with essentially no filler.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a single-integer predicate with full annotation coverage and no output schema, the description supplies definition, examples, domain limit, and access/pricing details. Only the return shape (true/false) is left implicit, which is a minor omission for a yes/no tool.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

There is one parameter with 0% schema description coverage, so the description must carry the load. It does establish that n is the tested integer and that 'n runs from 1 to 1000000' — but that range merely restates the schema's min/max, adding no type or edge-case meaning beyond it.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a precise mathematical predicate ('whether n is a product of three distinct primes') and disambiguates it with positive examples (30, 42, 66, 70) and negative ones (12, 60) with the reason ('square factor'). An agent can tell this apart from adjacent siblings such as squarefree, big_omega, or almost_perfect without opening any schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Usage is implied by the check semantics, but the description never says when to prefer this over the many related factorization siblings (squarefree, big_omega, divisor_count) that could partially answer the same question. No exclusions or alternative-routing guidance is given.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.