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

With no annotations, the description carries the full burden of behavioral disclosure. It explains the mathematical definition, but does not state what the tool returns, how the input value is supplied, or any edge-case behavior. The phrase 'Provide value' is ambiguous and does not clarify invocation behavior.

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 and front-loads the core purpose and definition. The only waste is the redundant 'Is Emirp:' prefix that echoes the tool name, and the vague 'Provide value' instruction, which is unhelpful.

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 tool that must accept a number and return a boolean-like result, the description is incomplete: it does not specify how the required value is communicated nor what successful output looks like. Since there is no output schema and no annotations, the description alone needed to make invocation unambiguous, and it does not.

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 properties, yet the description clearly requires a numeric value to check. 'Provide value' is not a meaningful parameter specification: it gives no argument name, type, format, or how the value should be passed. This is a critical gap because the schema provides nothing and the description fails to compensate.

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 clearly states the tool checks whether a number is an emirp and defines the term precisely: a prime whose reversal is also a different prime. However, it does not distinguish this tool from the similarly named sibling x402-is-emirp-number, so it only narrowly misses the top score.

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. Given near-identical siblings like x402-is-emirp-number and many other is-* predicate tools, the description gives the agent no basis for choosing this one over another.

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