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

No annotations are provided, so the description carries the full burden. It discloses a quota constraint ('5 free trial calls per signed wallet') but omits the return type (presumably boolean), edge-case behavior, and what counts as 'equal digit length' or repeated prime factors.

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 purpose is front-loaded in a single efficient sentence. The emoji and free-trial note add mild noise but do not obscure the core definition.

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?

With no output schema and no annotations, the description should explain the expected return value and input format. It defines the mathematical property but leaves an agent unsure how to format the parameter or interpret the response.

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 description coverage is 0% for the single 'value' parameter, and the schema types it as a string while the description only says 'integer.' This adds minimal semantic clarity and leaves format, size limits, and string-vs-number handling unexplained.

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?

States a precise mathematical predicate: 'Checks whether an integer has exactly two prime factors of equal digit length.' This clearly distinguishes it from siblings like x402-is-semi-prime or x402-prime-factors, though it does not explicitly name those alternatives.

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 on when to choose this over siblings like x402-is-prime or x402-is-semi-prime. The only additional sentence concerns free trial calls, which is pricing information rather than usage routing.

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