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

Annotations already declare readOnly/idempotent/non-destructive/openWorld, so the safety profile is covered. The description adds genuinely non-obvious behavioral facts: a per-call price of $0.001 USDC via x402 on Solana and an equivalent HTTPS endpoint. It does not mention latency or failure/refund behavior on failed calls, which is the main remaining gap for 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?

Purpose first, then worked examples that carry the semantics, then domain, then price/endpoint. Four short sentences with no filler; the numeric examples are doing real disambiguation work rather than 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?

No output schema exists, yet the description effectively communicates return values by example (0, 1, 3, 7 for the given inputs), and the cost/transport details are included. For a one-parameter pure function this is complete enough for an agent to call it correctly in one shot.

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%, so the description must carry the load. It does: 'n runs from 1 to 10000' restates the bounds, and the boundary examples (560 → 0, 561 → 1, 1729 → 3, 10000 → 7) make the inclusive-upper-bound meaning of n unambiguous. What it does not clarify is behavior at edges beyond restating the schema's min/max.

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?

Opens with a precise verb+resource statement ('How many Carmichael numbers are at most n'), which cleanly separates it from siblings like carmichael_next or carmichael_sum by virtue of the counting verb. It never names those siblings though, so an agent must infer the distinction from the verb alone.

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 valid input domain (1 to 10000) and the inclusive 'at most n' semantics are stated explicitly, and the worked examples pin down the counting convention (0 through 560, 1 through 561). There is no explicit guidance about which sibling to prefer for related queries, but for a single-parameter pure function the selection context is adequately clear.

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