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

The annotations already declare readOnlyHint, idempotentHint, openWorldHint, and destructiveHint=false. The description adds useful behavioral context: pricing per successful call, x402/Solana payment, and an equivalent HTTPS endpoint. It does not contradict the annotations, though it could state the boolean return value more explicitly.

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 description is front-loaded with the core definition, followed by concise examples, bounds, and necessary payment/access information. Every sentence contributes to correct invocation or interpretation.

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 simple two-parameter predicate with no output schema, the description is largely complete: it defines the property, gives examples including the n=1 edge case, and states bounds. The main minor gap is that it does not explicitly say the result is a boolean true/false.

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 parameter meaning. It defines n and y through the rough-number property, provides clarifying examples, and states the numeric range for both parameters. It does not give separate per-parameter descriptions, but the semantics are otherwise clear.

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 n is y-rough, defined as having smallest prime factor at least y. Examples clarify the definition. It does not explicitly distinguish this tool from related siblings such as smooth, powersmooth, or smallest_prime_factor.

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?

The description explains what the tool computes but gives no guidance on when to use it instead of related tools. There are no explicit alternatives, exclusions, or usage conditions beyond the mathematical definition itself.

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