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

Annotations already declare readOnly/idempotent/non-destructive, so the bar is lower. The description adds genuinely new context: a per-call price with the x402/Solana payment mechanism and an equivalent HTTPS endpoint, which affects call planning. It omits what is returned on failure (e.g., even n rejection), keeping it from a 5.

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, followed by clarifying examples (7, 9, 27), then constraints, then pricing/endpoint. The three worked examples earn their place by disambiguating 'lexicographically smallest', though the range restatement is redundant against the schema.

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-parameter, no-output-schema tool, the description covers computation, input domain, cost, and an alternate transport, which is enough to invoke it correctly. The exact response shape is only implied by 'triple of primes', which is acceptable but not spelled out.

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%, so the description must carry the load, and it adds a meaningful constraint not encoded in the schema: n must be odd. It also restates the 7–9999 range, though that duplicates the schema's minimum/maximum. No error semantics for violating the oddness rule are given.

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 first sentence gives a specific verb-like computation ('lexicographically smallest triple of primes adding to an odd n'), which is precise and distinguishable from broad siblings like goldbach_check or goldbach_count. It does not name those siblings explicitly, but the 'odd n' + 'smallest triple' framing makes the output shape 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?

Usage is implied by the constraint 'n is odd, from 7 to 9999', which tells the agent when the input is valid. There is no explicit statement of when to choose this over goldbach/goldbach_check or what happens for even n, so routing guidance is only implicit.

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