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

Annotations already declare readOnly, idempotent, non-destructive, openWorld, so the safety profile is covered. The description adds context the annotations cannot: the domain bound (1–2000), the per-call price, the x402/Solana payment requirement, and a parallel HTTPS endpoint — all material to whether an agent should call this at all.

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?

Front-loaded with the predicate, then constraints, then cost and endpoint — a sensible order with no filler. The telegraphic example phrasing ('945 is. 1, 9, and 15 are not') is compact but slightly clipped; every remaining clause earns its place.

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 one-parameter predicate tool with no output schema, the description conveys enough: it frames the result as a yes/no question, bounds the input, and discloses the payment model. It does not explicitly state the return type or error behavior for out-of-range n, but nothing critical is missing.

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?

Schema coverage is 0% and the schema only carries min/max, so the description must supply the meaning of n. It does so by restating the 1–2000 range and by anchoring values with worked examples (945 true, 1/9/15 false, 6 false), which is meaningfully more than the schema alone.

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?

Opens with a precise predicate ('Whether n is an odd Zumkeller number') and immediately disambiguates the 'odd' qualifier by noting that an even Zumkeller number like 6 answers false, which separates it from the sibling 'zumkeller' tool. An agent knows exactly what question this tool answers.

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?

The examples (945 true; 1, 9, 15 false) and the 1–2000 range give usable context for when the tool applies, but there is no explicit routing statement naming alternatives such as zumkeller, zumkeller_subset, or zumkeller_count. Usage is implied rather than spelled out.

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