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

Annotations already declare readOnlyHint, idempotentHint, and destructiveHint=false, so the safety profile is covered. The description usefully adds pricing ($0.001 USDC per successful call via x402 on Solana) and an equivalent HTTPS endpoint — real context not available in structured fields. It does not, however, say what the response looks like (boolean, JSON field name), which matters for a paid predicate call.

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 in the first sentence, followed by examples and then the commercial details, with no filler. The restatement of the 1–1000000 range duplicates the schema bounds and is the only clearly redundant clause.

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?

With no output schema and a predicate-style tool, the description should state the return value; it only implies a yes/no result. The domain and pricing are covered, so an agent can likely call it correctly, but the response shape is left to inference.

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?

The single parameter has 0% schema description coverage, so the description must carry the load. It does state the domain ('n runs from 1 to 1000000'), but that only restates the schema's minimum/maximum, and it never explicitly identifies n as the integer under test nor explains behavior at the boundaries.

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?

The description gives a precise mathematical predicate — 'n has no zero digit and the product of its digits divides n' — with concrete positive and negative examples (1, 11, 24 qualify; 10, 13, 22 do not), so an agent knows exactly what property is being tested. It never says the tool returns a boolean answer for a single n, and it does not name the sibling zuckerman_count, but the property definition is unambiguous.

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?

There is no when-to-use guidance and no mention of alternatives, even though zuckerman_count is an obvious sibling covering the counting variant. The examples of qualifying/non-qualifying numbers help an agent sanity-check inputs, but do not tell it when to pick this tool over another.

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