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

Annotations already declare readOnlyHint, idempotentHint, and destructiveHint=false, so the safety profile is covered. The description adds genuinely useful non-schema behavior: a per-call price ($0.001 USDC via x402 on Solana) and an alternate HTTPS endpoint, which an agent needs to know before invoking a paid tool.

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 property definition is front-loaded, followed by compact qualifying/non-qualifying examples, then the domain and payment/endpoint metadata. Every sentence carries information; nothing is padding.

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 no output schema, the description covers the domain, semantics, cost, and alternate transport. The one gap is the return value: it never says the result is a boolean true/false or what shape the response takes.

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 coverage is 0% (the single parameter has only min/max bounds, no description), so the description must compensate. It does by stating that n runs from 1 to 1000000000 and, via the worked examples, clarifying that n is the integer being tested — matching the schema's constraints.

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 the exact mathematical property in specific terms (all digits nonzero, all distinct, each digit divides n) and reinforces it with qualifying (12, 15, 24, 124, 135) and non-qualifying (10, 11, 13) examples. No sibling tool evaluates this predicate, so the definition alone is enough to tell it apart.

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 examples convey what counts as a Lynch Bell number and the input domain is bounded (1 to 1000000000), which implies the check is only meaningful for positive integers. But there is no explicit when-to-use/when-not guidance, no mention of alternatives, and no statement of what happens for out-of-range input.

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