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

Annotations already mark the tool as read-only, idempotent, non-destructive, and open-world. The description adds useful behavioral context not in the annotations, notably the search stopping condition (20 steps or 12 digits) and the per-call price, though it does not clarify what is returned if the search limit is reached.

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 short, front-loaded, and mostly free of waste. The examples, search limits, range, and payment details all serve a purpose, though the opening phrase could more explicitly state the action being performed.

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 one-parameter mathematical tool with rich annotations, the description covers input range, examples, and search limits. However, with no output schema, it does not fully specify the return value or what happens if the 20-step/12-digit limit is reached, leaving an important behavioral gap.

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 n. It states the valid range 2 to 10000 and gives worked examples mapping inputs to outputs, which meaningfully supplements the bare integer schema.

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 identifies the specific mathematical resource (the home prime of n) and clarifies it with worked examples such as 4 -> 211 and 10 -> 773. It does not explicitly differentiate from nearby sibling tools like home_prime_len or home_prime_steps, keeping it below 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?

It gives the input range and search limits but does not say when to use this tool versus alternatives such as home_prime_len, home_prime_steps, or home_grows. The agent is left to infer its role from the name and examples alone.

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