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

No annotations are provided, so the description carries the full behavioral burden, and it discloses nothing: not whether the result is a list, a boolean, a count, or an enumeration bound; not whether it is read-only; not how n/limit interact.

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?

Extremely short, but this is under-specification rather than conciseness: the single phrase repeats the title and earns no informational place.

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 2-parameter math tool with no annotations, no output schema, and a dense sibling cluster of perfect/abundant/deficient helpers, the definition is completely inadequate to call the tool correctly.

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 nominally 100%, which sets the baseline at 3, but the schema text ('N to process', 'Limit to process') is vacuous and the description adds nothing about what n vs limit mean (starting point vs count vs upper bound).

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 'Perfect Numbers: Perfect Numbers' merely restates the tool name with no verb, scope, or output form (list of perfect numbers? test? nth?). Siblings such as x402-is-perfect, x402-is-perfect-number, and x402-abundant-numbers make the missing differentiation especially costly.

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 exclusion of the many is-perfect / abundant / deficient siblings, and no statement of what inputs are expected. An agent has nothing to route on.

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