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

Annotations already declare readOnly, idempotent, non-destructive, and openWorld behavior; the description adds cost ($0.001 USDC per successful call), payment protocol (x402 on Solana), and an HTTPS endpoint. It does not explicitly state the return type or failure behavior, so it is strong but not complete.

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-loads the definition, then examples, range, and payment/access details. Each sentence has a clear purpose and there is no filler.

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 predicate, it supplies the mathematical definition, examples, domain, and cost/access details. No output schema exists, and the only notable missing piece is an explicit true/false return statement.

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?

There is one parameter, n, with 0% schema description coverage. The description restates its domain (1 to 1000000000000) and gives example values, which compensates for the missing schema description, though it adds little beyond the schema's min/max and integer type.

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 the exact predicate ('Whether n is refactorable') and defines it mathematically, with examples of true and false cases. This is a specific verb/resource and distinguishes it from divisor-related siblings by the property being tested.

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 implies when the tool is applicable by defining the property, but it never explicitly says to use this instead of divisor_count/divisor_sum or other alternatives. No when-not conditions or sibling routing are provided.

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