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

With no annotations, the description carries the full burden. It usefully discloses the exact property being tested and the x402 payment context ('5 free trial calls per signed wallet'), but says nothing about invalid/non-integer input handling, the boolean return, or any cost after the trial. This is decent disclosure but not complete for a no-annotation tool.

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 property definition in one tight clause, followed by the trial-credit note. Efficient overall, though the emoji-laden promo sentence is marginal content for an agent choosing a 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?

For a trivial one-parameter predicate with no output schema or annotations, the definition plus pricing note is nearly sufficient. The main omission is an explicit statement of the return value (true/false), which 'Checks whether' only implies.

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% and the single parameter ('value', typed string, not even required) is unexplained. The description at least establishes that the input should be an integer, adding a small amount of meaning over the bare schema, but it does not resolve the string-vs-integer mismatch or requiredness.

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 specific verb ('Checks whether') and gives a precise mathematical predicate: composite and passing the Fermat congruence for every coprime base. That condition distinguishes it from neighbors like x402-is-pseudoprime (single base) and x402-carmichael-function (which computes lambda rather than testing), even though those siblings are never named explicitly.

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 mathematical definition implicitly tells an agent what this tool answers, but there is no explicit when-to-use/when-not guidance and no routing to alternatives such as x402-carmichael-function or x402-is-pseudoprime. Usage is inferable rather than stated.

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