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

No annotations are provided, so the description alone must disclose behavior. It discloses nothing beyond the tool name, omitting whether the tool checks a number, what input it expects, what output it returns, or any side effects. This fails to satisfy the behavioral burden.

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 but only repeats the name verbatim. This is under-specification rather than conciseness; every sentence should earn its place, and this one adds no information.

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?

Despite the simple domain, the tool has no annotations, no output schema, and a description that is a tautology. An agent receives no explanation of inputs, outputs, or semantics, making the definition completely inadequate for correct invocation.

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?

The input schema has zero parameters and schema description coverage is 100%, so there are no parameter semantics for the description to clarify. The baseline for a zero-parameter tool is 4; the description adds nothing but nothing is required.

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 Num: Is Fermat Prime Num' is a pure restatement of the tool name and title. It does not state a verb, a resource, or any functional behavior, and it fails to distinguish this tool from closely related siblings such as x402-is-fermat or x402-is-fermat-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 guidance about when to use this tool versus alternatives like x402-is-prime, x402-is-fermat-prime, or x402-is-mersenne-prime. The description provides no context, no conditions, and no exclusions, leaving the agent to infer everything from the name.

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