is_safe_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 describes the mathematical check but lacks behavioral details such as input validation (e.g., handling non-prime q, negative numbers, or large integers), performance characteristics, error handling, or return format. The description is minimal and does not compensate for the absence of annotations.

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 highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by domain/category tags. There is no wasted text, and every element (definition and context) earns its place efficiently.

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 tool's low complexity (1 parameter, no output schema, no annotations), the description is minimally adequate. It defines the safe prime check but lacks details on output (e.g., boolean result or additional info), error cases, or usage examples. For a simple mathematical tool, it meets basic needs but could be more informative to fully guide an 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 with 0% description coverage. The description adds meaning by specifying that 'q' is a prime number to check for safe prime status, which clarifies the parameter's role beyond the schema's type definition. However, it does not provide additional details like constraints (e.g., q must be positive) or examples, so it partially compensates for the 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 prime q is a safe prime (q = 2p + 1 where p is prime).' It includes a specific verb ('Check'), resource ('prime q'), and mathematical definition, clearly distinguishing it from sibling tools like 'is_prime' or 'is_sophie_germain_prime' by focusing on the safe prime property.

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 clear context with the domain and category tags ('Domain: arithmetic, Category: special_primes'), indicating it's for arithmetic operations on special primes. However, it does not explicitly state when to use this tool versus alternatives like 'is_sophie_germain_prime' or other primality tests, nor does it mention prerequisites (e.g., that q must be prime).

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