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

Annotations already cover read-only, idempotent, non-destructive, and open-world, so the description focuses on added context: the $0.001 USDC x402 cost per successful call and the equivalent HTTPS POST endpoint. The example count values also tell the agent what kind of bounded scalar result to expect, which the absent output schema would otherwise not supply.

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?

Purpose is front-loaded in the first clause, followed by illustrative examples, then the valid range, then pricing and the alternate endpoint. It is dense but every sentence carries information; the only redundancy is the range restatement already encoded in the schema.

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, no-output-schema tool, this is close to sufficient: it defines the count, bounds the input, illustrates expected return values, and discloses cost and transport. The main missing element is guidance on choosing it over the moran_* siblings.

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?

With schema description coverage at 0%, the description must carry the meaning of n, and it does establish n as the inclusive upper bound ('at most n') and illustrates it with sample inputs (1, 18, 21, 30, 100). However, the '1 to 2000' range merely restates the schema's minimum/maximum, so the net semantic gain is modest.

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: 'How many Moran numbers are at most n', which is an unambiguous counting operation. It is clearly distinct from the moran/moran_next/moran_sum siblings by virtue of being a count, but the description never names those siblings or states the differentiation explicitly.

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 gives worked example values but never says when to use this tool versus moran, moran_next, moran_ratio, or moran_sum. No exclusions, prerequisites, or alternative routing are provided, so the agent must infer selection from the name alone.

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