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

Annotations already declare readOnlyHint, idempotentHint, openWorldHint, and destructiveHint=false, so the safety profile is clear. The description adds meaningful context beyond annotations: the price per successful call, the HTTPS endpoint, and the valid input range. It does not contradict annotations.

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 description is compact and front-loaded: purpose first, then examples, range, price, and endpoint. Every sentence adds useful information for an agent deciding whether and how to call the tool. 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?

For a one-parameter lookup with no output schema, the description is complete enough: it defines the return value semantics (index or 0), the input domain, and the paid-call context. Annotations cover the read-only/idempotent safety profile. Nothing critical is missing for correct invocation.

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 parameter meaning. It does so by explaining that p runs from 2 to 6221671 and by giving concrete examples of how values map to indices, including 0 for non-members. The schema supplies type and bounds, but the examples add needed semantic clarity.

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 specific operation: finding where a number p sits among the first eight Euclid-Mullin primes, with 0 for non-members. The examples clarify the mapping directly. It does not explicitly name or distinguish alternatives like euclid_mullin, euclid_mullin_sum, or euclid_mullin_prod, but the index semantics are clear enough for selection.

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 and range imply when the tool is useful, but there is no explicit guidance on when to choose this index tool instead of sibling Euclid-Mullin tools. No when-not-to-use conditions or alternatives are stated. Usage is inferable but not fully directed.

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