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

No annotations are provided, so the description carries the full burden. It discloses nothing about the return value (boolean?), input constraints, or error behavior, leaving the agent with no behavioral information at all.

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?

It is short, but the brevity is under-specification rather than conciseness — the single sentence is a redundant echo of the name and contains no useful information. There is nothing to be front-loaded because nothing substantive is said.

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 math-predicate tool with no annotations, no output schema, and a generically described parameter, the description is completely inadequate. An agent cannot determine input type, output form, or how this differs from the many sibling primality tools.

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 coverage is nominally 100%, but the single parameter's schema description is the vacuous 'Value to process', and the type is string, which is odd for a primality test. The tool description adds no clarification of format, range, or expected input, so the schema baseline of 3 is not earned here.

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 'Is Fermat Prime: Is Fermat Prime' merely restates the tool name twice, which is a textbook tautology. It gives no verb+resource explanation beyond the name and offers zero differentiation from close siblings such as x402-is-fermat, x402-is-fermat-prime-num, or x402-is-mersenne-prime.

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?

There is no when-to-use guidance, no mention of alternatives, and no exclusions. An agent has no basis for choosing this over the near-identical x402-is-fermat-prime-num sibling besides the exact name.

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