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

Annotations already cover safety (readOnly, idempotent, non-destructive), and the description adds genuinely new behavioral facts: cost of $0.001 USDC per successful call via x402 on Solana, and an equivalent HTTPS endpoint. This is exactly the kind of context annotations cannot express. It stops short of stating any rate limits or latency expectations.

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-loads the definition, then anchors with examples, then the valid range, then commercial/transport details. No filler sentences. The pricing and endpoint lines are dense but each carries information an agent cannot get elsewhere.

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 single-parameter read-only math tool with no output schema, the description supplies the operation, the domain of n, and concrete expected outputs, which substitutes well for a missing output schema. Only the lack of sibling disambiguation keeps it from being fully complete.

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% and the schema only carries bare min/max, so the description must compensate. It does: it defines n as the count of Euclid-Mullin primes to multiply and anchors it with concrete example values (n=1→2, n=4→1806, n=7→6221670, n=8→38709183810570), which is more useful than the schema's numeric bounds.

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: 'the product of the first n Euclid-Mullin primes', which is more precise than the bare title 'Euclid Mullin Prod'. It does not explicitly differentiate from siblings like euclid_mullin, euclid_mullin_sum, or euclid_mullin_cofactor, so an agent must infer the distinction from the name.

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?

There is no guidance on when to use this tool versus the several euclid_mullin_* siblings, and no exclusions or prerequisites. The worked input/output examples are helpful for interpreting n, but they are parameter semantics, not usage routing.

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