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

Annotations already declare the operation as read-only, idempotent, non-destructive, and open-world. The description adds useful behavioral context beyond annotations by disclosing the per-call price, x402/Solana payment context, and an HTTPS alternative 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?

The description is compact and front-loaded: the core sequence term is stated first, followed by examples, the valid n range, and then pricing/transport details. Every sentence adds practical information for calling the tool.

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 simple one-parameter sequence-term lookup, the description covers the domain of n, gives example outputs, and explains payment/transport context. It does not explicitly state the return type or error behavior, but the examples and annotations make the tool sufficiently understandable.

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 states that n runs from 1 to 8 and supplies example values a(1), a(4), a(7), and a(8), which clarifies the indexing domain even though it partly duplicates the schema's min/max constraints.

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 identifies the resource as 'the nth Euclid-Mullin prime,' which is clearer than the bare tool name and is reinforced by concrete examples. It does not, however, differentiate this tool from sibling names like euclid_mullin_index, euclid_mullin_prod, or euclid_mullin_sum.

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 description states the valid range for n but gives no explicit guidance on when to use this tool instead of alternatives. With several Euclid-Mullin sibling tools present, the lack of routing guidance is a meaningful gap.

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