carmichael_number_test

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 tests for Carmichael numbers but doesn't disclose behavioral traits such as performance characteristics (e.g., computational complexity for large inputs), error handling (e.g., for non-integer or negative inputs), or output format. The description is minimal and lacks operational context.

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: a single sentence that directly states the tool's purpose. There's no wasted verbiage, and it efficiently communicates the core functionality. However, it could be more structured by including usage hints or parameter details without sacrificing brevity.

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 (testing for Carmichael numbers involves advanced primality concepts), lack of annotations, no output schema, and minimal parameter semantics, the description is incomplete. It doesn't explain what a Carmichael number is beyond 'pseudoprime to all bases', nor does it cover return values, error cases, or performance considerations, leaving significant gaps for an AI agent.

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 1 parameter 'n' with 0% description coverage (no schema descriptions). The tool description adds no parameter semantics—it doesn't explain what 'n' represents (e.g., a positive integer), valid ranges, or constraints. With low schema coverage, the description fails to compensate, leaving the parameter meaning unclear beyond the type 'integer'.

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: 'Test if a number is a Carmichael number (pseudoprime to all bases).' It specifies the verb ('Test'), resource ('a number'), and domain context ('advanced_primality'). However, it doesn't explicitly differentiate from sibling tools like 'is_carmichael_number' (which appears in the list), though the distinction might be in implementation details not described.

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 mentions the domain ('arithmetic, Category: advanced_primality') but doesn't specify prerequisites, when to prefer it over other primality tests (e.g., 'aks_primality_test', 'miller_rabin_test'), or any limitations. Usage is implied by the purpose statement alone.

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