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

Annotations already cover safety (readOnly, idempotent, non-destructive), but the description adds genuinely non-structured context: cost of $0.001 USDC per successful call via x402 on Solana, and an equivalent HTTPS endpoint. The 'per successful call' billing nuance and the payment rail are the kind of details an agent needs before invoking. Minor gaps: no note on failure/error behavior or whether a failed call is billed.

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?

Five compact sentences: definition first, then illustrative terms, then exclusions, then domain bound, then billing and the HTTPS alternative. Every sentence carries distinct information and the essential purpose is front-loaded.

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 one-parameter predicate with no output schema, this covers what the tool does, the valid input domain, the semantic examples, and the commercial terms — enough for correct invocation. The remaining hole is that return values are never described (presumably a boolean), and no sibling routing is given in a namespace of hundreds of overlapping number-theory tools.

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 carries the burden for the single parameter. It does restate the domain ('n runs from 1 to 100000'), which is useful reinforcement, but that range is already encoded as minimum/maximum in the schema, and it never explicitly states that n is the integer under test. Compensation is partial rather than thorough.

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 states a precise predicate: 'Whether n is a lucky number,' which cleanly separates it from siblings like lucky_nth, lucky_count, lucky_next, and lucky_twin even without naming them. It also seeds the concept with the first sequence terms and exclusion rules (5 and all evens), so the agent can sanity-check membership semantics. It stops short of explicitly contrasting itself with the sibling lucky tools.

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?

Usage is only implied by the predicate phrasing — an agent can infer 'call this when you need a yes/no membership answer for a single n.' There is no explicit when-to-use statement, no pointer to lucky_nth/lucky_count/lucky_next for related queries, and no exclusions. The example terms and the 'n runs from 1 to 100000' bound are the closest thing to guidance.

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