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

With no annotations, the description carries the full behavioral burden. It does disclose the return semantics (boolean true/false) and surfaces the payment model ('5 free trial calls per signed wallet'), which is useful context. However, it says nothing about how inputs are parsed, numeric size limits, or behavior on non-numeric input.

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?

One sentence, front-loaded with the predicate and its definition, followed by the pricing note. The emoji and trial-call pitch are mild noise but do not obscure the core meaning.

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 simple stateless predicate with no output schema and no annotations, the definition covers the what and the return type, which is most of the requirement. It is still missing the input contract (string format, valid range) and error behavior, which an agent needs to invoke it without trial and error.

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 single parameter 'value' has 0% schema description coverage, and the description only refers to it obliquely as 'the value'. It does not state that the argument is a string, whether it must be a positive integer, whether left-padding/whitespace is tolerated, or what happens for values beyond big-integer range.

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?

It names a specific predicate plus resource and even defines the term ('proper divisors sum to it'), so an agent knows exactly what boolean question is being answered. It does not distinguish itself from the near-identical siblings x402-is-perfect, x402-is-perfect-num, or x402-perfect-numbers, which is the only thing keeping it from a 5.

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 on when to call this versus the sibling variants (x402-is-perfect, x402-perfect-numbers), nor any stated prerequisites about the signed wallet required by the pricing line. Usage must be inferred entirely from the name.

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