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

No annotations are provided, so the description carries the full burden of behavioral disclosure, yet it offers none. It doesn't specify whether the check is Fermat-based, whether the base parameter selects a specific Fermat base, or what the boolean meaning is (true = is pseudoprime to the base). This is a complete gap for a math-predicate 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?

The description is a tautology ('Is Pseudoprime: Is Pseudoprime') that technically avoids verbosity but fails to convey any information. Brevity here comes from under-specification, not from efficient phrasing.

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?

No annotations, no output schema, and a description that repeats the title. For a tool with two string parameters whose meanings (base vs value) are semantically critical to the result, this is completely inadequate.

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 100% and each param has a description ('Base to process', 'Value to process'), which is minimal but present. However, those schema descriptions are near-meaningless placeholders and the tool description adds no clarification about whether 'base' is the Fermat base and 'value' the candidate number, which is the crucial semantic distinction for a pseudoprime test.

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 restates the name verbatim ('Is Pseudoprime: Is Pseudoprime'), providing no elaboration of what pseudoprimality means or how the check is performed. While the name hints at the operation (test whether a number is a pseudoprime), the description adds nothing and one could confuse it with siblings like x402-is-prime, x402-is-carmichael, or x402-miller-rabin.

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 when a pseudoprime test is preferred over e.g. x402-is-prime or x402-miller-rabin, and no exclusion criteria. An agent has no signal to differentiate this tool from dozens of primality-adjacent siblings.

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