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

Annotations already declare readOnlyHint=true, idempotentHint=true and destructiveHint=false, so the description doesn't need to re-argue safety. It does add genuinely new context annotations cannot express: a per-call price ($0.001 USDC via x402 on Solana) and an equivalent HTTPS endpoint. It stops short of describing the return value shape, which keeps 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?

The core predicate and qualifying examples are front-loaded, then domain, then price and endpoint — a sensible ordering with little waste. Slightly telegraphic in phrasing but every sentence carries information.

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 with no output schema, the description supplies the definition, positive and negative examples, the input domain, the cost, and an alternate transport. Nothing an agent needs in order to decide and invoke correctly 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 description coverage is 0%, so the description must carry the meaning of the single parameter, and it does: n is the integer under test and is bounded to 1..1000000. The examples also demonstrate the value format. It gains little beyond restating the schema's min/max, so not a 5.

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 states a precise mathematical predicate ('Whether no fourth power divides n') rather than restating the name, and the two example sets (1, 8, 12, 36 qualify; 16, 32, 48, 81 do not) make the semantics unambiguous. It does not explicitly distinguish itself from adjacent siblings like cubefree or squarefree, so it falls short of a 5.

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 only implied: the domain 'n runs from 1 to 1000000' and the examples tell an agent when the tool applies, but no alternative (e.g. squarefree, cubefree) is named and there is no statement of when NOT to use it. Adequate but leaves the agent to infer routing among many number-theory siblings.

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