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

Annotations already declare read-only, idempotent, non-destructive, and open-world behavior. The description adds useful context beyond annotations: the valid domain, deterministic examples, per-call pricing, and an HTTPS endpoint alternative. It does not describe error behavior, but the added commercial and endpoint details are substantial.

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 definition is front-loaded, followed by clarifying examples, domain range, pricing, and endpoint. Every sentence contributes directly to understanding or invoking the tool.

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?

This is a simple deterministic math tool with full annotation coverage and a clear return concept embedded in the definition. The description supplies all information needed to call it correctly, including range, inclusive behavior, pricing, and endpoint alternative.

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 compensate. It defines the domain of n as 2 through 10,000,000 and the examples clarify that the result is inclusive when n is prime, which adds meaning beyond the schema's type and bounds.

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 function: the greatest prime less than or equal to n, with concrete examples clarifying the inclusive boundary. This is specific enough to distinguish it from sibling prime tools such as next_prime or prime_check.

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 makes the operation clear and gives examples, so usage is implied, but it does not explicitly name alternatives or state when to use this instead of next_prime, prime_nth, or prime_check. A competent agent can infer the use case, but the routing guidance is not explicit.

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