is_fermat_prime

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

No annotations are provided, so the description carries the full burden. It states the tool's function but does not disclose behavioral traits such as performance characteristics, error handling, input constraints (e.g., valid ranges for 'n'), or output format. This is inadequate for a tool with no annotation coverage.

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 a single, efficient sentence that front-loads the core purpose without unnecessary words. The parenthetical domain and category add useful metadata without clutter, making it highly concise and well-structured.

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?

Given no annotations, no output schema, and low parameter coverage, the description is incomplete. It explains what the tool does but lacks details on behavior, input constraints, and output format, which are essential for a mathematical verification tool. The domain/category hint helps but does not fill these gaps.

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?

The input schema has 0% description coverage, with one parameter 'n' of type integer. The description adds some semantic context by implying 'n' is used in the formula 2^(2^n) + 1, but it does not specify valid ranges, units, or examples. This partial compensation aligns with the baseline for low schema coverage.

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 explicitly states the tool's purpose: 'Check if a number is a Fermat prime (prime of form 2^(2^n) + 1).' It includes a specific verb ('Check'), resource ('number'), and mathematical definition, clearly distinguishing it from siblings like 'is_prime' or 'fermat_primality_test' by focusing on the special Fermat prime form.

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 provides no guidance on when to use this tool versus alternatives. It lacks any mention of prerequisites, typical use cases, or comparisons to sibling tools like 'fermat_primality_test' or 'is_prime', leaving the agent without context for selection.

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