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

Beyond the readOnly/idempotent annotations, the description discloses pricing ($0.001 USDC per successful call, x402 on Solana) and an equivalent HTTPS endpoint, which is real operational context an agent needs before calling. It does not describe the return type explicitly, but the worked examples effectively demonstrate the output.

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 purpose in the first sentence, followed by concrete result examples, the domain, and pricing. Dense but every sentence contributes; the pricing/endpoint line is slightly tacked-on but useful.

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 read-only predicate with no output schema, the description covers domain, sample answers that imply a boolean return, and access/pricing details. Only the exact return shape and out-of-range behavior are left unstated.

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 parameter meaning. It does state 'n runs from 0 to 11', which clarifies n as the index of the Apery number, but this largely repeats the min/max already present in the schema and adds no unit or edge-case detail.

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?

States a specific predicate over a named resource: whether the Apery number A(n) is prime. An agent can easily separate it from siblings like apery (which presumably returns the value itself) or apery_sum. It does not explicitly name the sibling to use for the raw value, keeping it just 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 implied by the 'whether ... is prime' phrasing and the stated domain n = 0..11, but there is no explicit when-to-use/when-not guidance and no named alternative (e.g., prime_check for general primality). The agent must infer the boundary conditions.

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