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

Annotations already establish that this is a safe, read-only, idempotent computation. The description adds useful context beyond annotations: it states the pricing model, payment network, and HTTPS endpoint alternative, and examples show the input-to-output behavior.

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 front-loaded with the core definition, then examples, then range and access/pricing details. Every sentence contributes useful information, with 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 simple one-parameter math tool with rich annotations and no output schema, the description is largely complete: it explains the computation, gives examples, specifies the valid range, and notes pricing/endpoint details. Only an explicit statement of the return type or error behavior is missing.

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 only one parameter and 0% schema description coverage, the description compensates by stating the valid range and giving several example mappings such as 14 -> 19 and 17 -> 19. These examples clarify the 'at least n' rounding-up semantics beyond the bare integer bounds in the schema.

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 defines a specific mathematical operation: the smallest Higgs prime with exponent 2 that is at least n, and gives concrete examples. It is clear what value is computed, but it does not explicitly distinguish itself from nearby siblings such as higgs, higgs_index, or higgs_gap.

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 the valid input range and examples, but no explicit guidance on when to choose this tool over alternatives like higgs, higgs_index, or higgs_count. The usage is implied by the function itself rather than stated.

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