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

Annotations already declare read-only, idempotent, non-destructive behavior, so the description is not the sole source of safety context. It adds genuinely useful operational detail beyond annotations: the valid input range, the $0.001 USDC per-successful-call cost via x402 on Solana, and an HTTPS endpoint alternative. It does not explicitly say the result is a boolean, but 'Whether...' strongly implies it.

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 core predicate is front-loaded, followed by compact examples and then pricing/endpoint boilerplate. Sentence fragments are efficient, though the payment and URL details could be trimmed or moved to a note.

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 single-parameter predicate tool with annotations and no output schema, the description covers the concept, examples, input range, and payment model. The main gap is not stating the return type (true/false) explicitly, which is minor.

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%, so the description must carry the parameter meaning. It says n runs from 1 to 1000000, which restates the schema's min/max rather than adding new semantics, and it never explicitly defines n as the integer being tested for extravagance, though that is inferable from context.

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 specific predicate: whether the written factorization of n uses more digits than n, backed by concrete examples (4, 6, 12 yes; 10, 125 no). This distinguishes the concept clearly, though it never names the complementary siblings (frugal, equidigital) that an agent might otherwise confuse it with.

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?

The definition plus examples imply when the tool applies, but there is no explicit guidance on when to choose it over related siblings like frugal or equidigital, nor any exclusions. Usage is inferable rather than stated.

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