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

Annotations already cover read-only, idempotent, non-destructive behavior, so the description's real contribution is the costly-call disclosure: $0.001 USDC per successful call via x402 on Solana, plus an equivalent HTTPS endpoint. That payment requirement is operationally critical and nowhere in the annotations or schema.

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 definition and examples, then constraints, then access/pricing details. Three illustrative examples is slightly more than needed, but each sentence carries information an agent can act on.

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?

No output schema exists, yet the phrasing 'how many Goldbach splits' plus the numeric examples make the integer return value unambiguous. Combined with the domain constraint and payment/endpoint info, an agent has enough to call it correctly; only odd-n behavior is left open.

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 description coverage is 0%, but the single parameter is bounded in the schema and the description adds the semantic constraint that n must be even (the schema's 4-10000 range alone would admit odd values). Examples further anchor the meaning of the parameter, though nothing is said about behavior for odd n.

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 names a specific computation (count of Goldbach partitions with p <= q) and pins it down with worked examples (10→2, 20→2, 100→6). It is clearly distinguishable in substance from the sibling 'goldbach'/'goldbach_check' tools, though it never names them explicitly.

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?

It states the input domain (n even, 4 to 10000), which implicitly scopes when the tool applies, but gives no explicit when-to-use versus the closely-named siblings goldbach, goldbach_check, or odd_goldbach. The agent must infer the choice from the tool names alone.

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