fermat_primality_check

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does without explaining how it behaves—e.g., whether it returns a boolean, an error for invalid inputs, performance characteristics, or mathematical assumptions (like the probabilistic nature of Fermat tests). 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 concise and front-loaded, consisting of a single sentence that states the core purpose followed by domain/category tags. There is no wasted text, and it efficiently communicates the essential information in a structured manner.

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 the complexity of a primality test tool with no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not explain the tool's behavior, parameter meanings, return values, or error handling, making it insufficient for an AI agent to use the tool effectively without additional context.

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 2 parameters (n and a) with 0% description coverage, meaning the schema provides no semantic information. The description mentions 'base a' but does not explain what 'n' represents (likely the number to test) or the roles, constraints, or expected ranges of either parameter. It adds minimal value beyond the schema, failing to compensate for the coverage gap.

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 clearly states the tool's purpose: 'Perform Fermat primality check for base a.' It specifies the verb ('Perform'), resource ('Fermat primality check'), and scope ('for base a'), making it understandable. However, it does not explicitly differentiate from its sibling 'fermat_primality_test', though the distinction might be implied by the parameter focus.

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 minimal guidance: it mentions the domain ('arithmetic') and category ('primality_tests'), which gives some context. However, it lacks explicit instructions on when to use this tool versus alternatives (e.g., 'fermat_primality_test' or other primality tests like 'aks_primality_test'), prerequisites, or limitations, leaving usage unclear.

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