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

No annotations exist, so the description carries the full burden. 'Checks whether' correctly implies a read-only predicate, and the '5 free trial calls per signed wallet' line is genuine added behavioral context (paywall/rate limit) that structured fields do not provide. It still says nothing about output shape, handling of non-numeric strings, or failure modes, so the disclosure is partial.

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 functional statement is front-loaded and compressed into a single clause with a precise definition. The trailing promo/emoji about free trial calls is non-functional noise, but small enough that it doesn't bury the core content.

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 one-parameter boolean predicate with no annotations and no output schema, the description covers the definitional ambiguity, which is the main risk. It still leaves the return value, accepted input format, and the sibling overlap unaddressed, so it is adequate but not complete.

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?

One parameter named 'value' with 0% schema coverage, so the description must compensate. Saying 'value' holds a number whose prime factorization is tested does constrain meaning, but it omits the fact that the schema types it as a string and gives no format, range, or sign guidance. Marginal compensation for a fully undocumented parameter.

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 gives a specific verb ('Checks whether') and resource ('value'), and goes further by stating the exact mathematical criterion (every prime factor p satisfies p² | value). That is enough for an agent to know exactly what the tool computes. However, it does not distinguish itself from the near-identical sibling x402-is-powerful, leaving selection between the two ambiguous.

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 or when-not-to-use guidance, no mention of inputs that are invalid, and no pointer to the near-duplicate sibling x402-is-powerful. The agent gets a definition but no routing context.

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