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

Annotations already cover read-only/idempotent safety, and the description adds genuinely new behavioral context: rejection of non-Carmichael inputs, the valid domain of n, the paid model ($0.001 USDC per successful call via x402 on Solana) and an equivalent HTTPS endpoint. Cost and payment rail are the kind of prerequisite an agent cannot get from annotations. It stops short of describing the error response shape when n is rejected.

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?

Front-loaded with the exact output contract before any examples or constraints. Three worked examples for the same simple mapping is slightly more than strictly needed, but each is short and they remove any ambiguity about ordering and separators, so nothing reads as 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?

With no output schema and no annotation coverage of results, the description has to define the return value itself — and it does fully (ascending, comma-separated prime factors, with examples). Combined with the domain limit, rejection behavior and payment terms, an agent has everything needed to decide and call correctly.

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?

There is a single parameter with 0% schema description coverage, so the description must carry the semantics — and it does: n is the Carmichael number to factor, bounded 1–20000, and the three examples (561→3,11,17 etc.) make the n-to-output mapping unambiguous. The range detail is redundant with the schema's minimum/maximum, and the meaning of n as the input value itself is only implied by the examples.

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 concrete verb+resource: it returns the prime factors of a Carmichael number, with output ordering (ascending) and format (comma-separated) spelled out. It does not explicitly contrast itself with the nearby siblings carmichael, carmichael_number, carmichael_count or carmichael_sum, so the agent must infer the distinction from the word 'factors'.

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?

It supplies real usage constraints: n must be an actual Carmichael number (non-Carmichael inputs are rejected) and n must fall in 1–20000, plus worked examples. However, no alternative is named — it never says to use carmichael, prime_check or a general factorization tool when the input is not Carmichael, which is exactly the decision point an agent faces in this crowded sibling set.

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