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

With no annotations provided, the description carries the full burden of behavioral disclosure and fails completely. It doesn't state what inputs the check consumes (the schema is empty), what it returns, what happens on edge cases like non-coprime bases, or whether any side effects occur.

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 text is under-specified rather than concise: 'Is Primitive Root' is repeated verbatim in a 'Label: Label' template, wasting the only opportunity to convey meaning. Brevity that delivers zero information does not earn a high conciseness score.

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?

The tool is a mathematical predicate operating in a crowded domain of related tools, yet the description is two identical phrases. With an empty input schema, no output schema, and no annotations, an agent has no path to figure out what inputs to supply or what result to expect.

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 schema has zero parameters, so per the baseline rule the description bears no duty to document them. However, a primitive-root predicate semantically needs at least a base and a modulus, so the unexplained empty schema is a latent usability defect; that gap is better scored under contextual completeness.

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 Primitive Root: Is Primitive Root' is a pure tautology that restates the tool name without adding a verb, resource, or scope. It doesn't say what the tool computes, what mathematical inputs it requires, or how it relates to the dozens of number-theory siblings like x402-is-quadratic-residue or x402-pow-mod.

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?

No guidance is given on when to invoke this tool versus alternatives. The sibling list contains closely-related modular arithmetic tools (x402-legendre-symbol, x402-euler-totient, x402-multiplicative-inverse, x402-pow-mod), and the description offers no decision criteria for choosing among them.

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