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

Annotations already declare readOnly/idempotent/openWorld safety, so the bar is lower; the description still adds economically important behavior — a $0.001 USDC charge per successful call via x402 on Solana and an HTTPS alternative endpoint. What it does not state is failure behavior (e.g., what happens for n values with no Carmichael number above them) or response shape beyond the examples.

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 definition, then examples, then constraints, then pricing/endpoint. Every sentence carries information an agent needs; there is no filler.

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, but the examples effectively reveal the return type (an integer Carmichael number). Payment mechanics and input range are covered. Minor gap: no statement about out-of-range or no-result cases, which matters for a bounded-domain tool.

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, and it does: it restates the valid domain (1 to 10000) and, more usefully, gives four input/output exemplars that pin down the 'at least n' boundary convention. Only the boundary edge behavior at n=10000 is left unstated.

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 mathematical relation — 'the smallest Carmichael number that is at least n' — which is far more precise than the name alone and clearly separates it from siblings like carmichael, carmichael_count, and carmichael_number. Worked examples (561 at n=1, 1105 at n=562) make the semantics unambiguous.

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 implied by the semantics: use it to get the next Carmichael ≥ n rather than to test membership. But given a sibling set containing carmichael, carmichael_number, carmichael_factors, and carmichael_count, the description never explicitly routes the agent away from those alternatives.

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