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

With no annotations and a tautological description, the tool's behavior is completely undisclosed. The agent cannot know whether this tests Fermat primes, Fermat numbers, Fermat's little theorem, or something else, nor what output to expect.

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 technically short, but it is under-specified repetition rather than genuine conciseness. 'Is Fermat: Is Fermat' wastes its only sentence and fails to convey any useful 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?

Even though the tool has no parameters, it still needs a purpose statement and expected behavior. With no annotations, no output schema, and only a tautological description, the agent lacks the basic information needed to select and invoke this tool correctly.

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, so there are no parameter semantics for the description to explain. The baseline for a no-parameter tool is 4, and the description does not need to add parameter detail; however, it also contributes nothing about how the implicit input is supplied.

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 'Is Fermat: Is Fermat', which merely restates the tool name and provides no verb, resource, or domain. It does not define what 'Fermat' means here or how this tool differs from siblings like x402-is-fermat-prime or x402-is-fermat-prime-num.

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 the many related Fermat and number-checking siblings. The description provides no context, prerequisites, or exclusion criteria, leaving the agent to guess entirely from the name.

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