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 still adds real behavioral context beyond them: inputs outside the Blum class are rejected rather than returning an error-free empty result, the output is ordered smallest factor first, and there is a per-call cost of $0.001 USDC via x402 plus an HTTPS fallback endpoint.

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 semantics of the return value, then constraints, then cost — a sensible ordering with no filler sentences. Three worked examples is one more than strictly necessary, but they are short and each reinforces the ordering convention.

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?

There is no output schema, and the description fully compensates by specifying the shape of the return (two factors, smaller first) with examples. It also covers the input domain, the rejection behavior on invalid input, the pricing model, and an alternate transport, leaving nothing an agent needs in order to call it 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?

Schema coverage is 0%, so the description must carry the meaning of n, and it does: n is bounded 1–1,000,000 and must be a Blum integer or the call is rejected. The worked examples further pin down what a valid input looks like. It stops short of explaining what happens for small edge cases on the boundary of the domain.

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 verb and resource: it returns the two prime factors of a Blum integer, smaller factor first. Worked examples (21 → 3,7) make the semantics of the output unambiguous. It does not, however, name the closely related siblings (blum, blum_count, blum_next, largest_prime_factor, smallest_prime_factor) so the agent cannot tell from the description alone which one it wants.

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 domain constraint 'non-Blum integer is rejected' and 'n runs from 1 to 1000000' implicitly tell the agent when this call will fail, which is useful guidance. But there is no explicit when-to-use/when-not framing and no routing to alternatives such as the blum membership test or general factor tools, so the agent must infer selection from the name.

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