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

Annotations already declare readOnly, idempotent, non-destructive and open-world, so the safety profile is covered. The description adds material context those annotations omit: a hard input bound of 1 to 1e12, a per-call price of $0.001 USDC via x402 on Solana, and an equivalent HTTPS endpoint — exactly the payment/auth context an agent needs before calling. It stops short of noting failure/charging behavior on invalid input.

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?

The definition is front-loaded in the first sentence, followed by illustrative examples, then operational details (range, price, endpoint) at the end where they belong. Every sentence carries information; the range is stated twice in effect (once in prose, once in the schema) but that is a minor redundancy.

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 one parameter, full annotation coverage and no output schema, the description gives enough to call the tool correctly: input domain, semantic definition, examples, and cost/transport. The one remaining gap is that the return type is only implied ('whether...are both prime') rather than stated as a boolean result, which matters slightly since no output schema exists.

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 must carry the parameter semantics — and it does, defining n's domain (1 to 1000000000000) and demonstrating with three concrete values what the parameter means and what the tool returns for each. It does not explain that out-of-range or non-integer input is rejected, which the schema enforces but the description never warns about.

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 the specific predicate it evaluates — whether n and 2n+1 are both prime — which is a precise verb+resource for a boolean math test, and the worked examples (2→5, 11→23, 7→15) remove any ambiguity about the definition. It does not explicitly differentiate itself from the sibling safeprime tool despite referencing the term 'safeprime' in an example, so an agent could still hesitate between the two.

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 examples (2, 11, 7) imply how to call it and the valid input range is stated explicitly, but there is no when-to-use/when-not guidance and the sibling safeprime is never named as the alternative for the related query. Usage is inferable rather than directed.

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