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 provides none. It does not state what input the tool expects, what output it produces, what a pseudoprime determination means, or any edge cases. Notably, the input schema has zero properties, so the mechanism by which the tool receives a number to test is entirely unexplained - a critical behavioral gap for a 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 short but this is under-specification, not conciseness. The 'Is Pseudoprime: Is Pseudoprime' format contains a redundant duplicated phrase that appears to be a template artifact, and the single line earns no place because it conveys zero 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?

For a predicate tool with no annotations, no output schema, an empty input schema, and a tautological description, the definition is entirely inadequate. An agent cannot determine what number to test, what a pseudoprime is in this tool's context, which primality test underlies it, or what the return value means - especially dangerous in a namespace crowded with nearly identical is-* predicates.

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 per the baseline for 0-param tools, there is nothing for the description to document about parameter semantics. However, the empty schema combined with the useless description leaves the agent unable to determine how input is supplied, a concern that falls more under contextual completeness than parameter semantics.

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 Pseudoprime: Is Pseudoprime' is a pure tautology - it merely restates the tool name with zero additional content. It never defines what a pseudoprime is (composite number passing a primality test), which base or test (Fermat, Euler, strong) is used, or how it relates to the many sibling primality tools like x402-is-prime, x402-miller-rabin, x402-is-fermat-prime, and x402-is-carmichael.

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 usage guidance is provided whatsoever. The agent is given no basis for choosing this tool over the dozens of closely related number-theory predicates in the sibling list (is-prime, is-safe-prime, is-sophie-germain, is-emirp, is-carmichael, miller-rabin). No conditions, examples, or alternative recommendations appear.

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