is_sophie_germain_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 of behavioral disclosure. It states the tool checks a condition but does not describe error handling (e.g., what happens if p is not prime or negative), performance characteristics, or output format. For a tool with no annotations, this leaves significant gaps in understanding its behavior beyond the basic function.

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 function and includes domain/category tags. There is no wasted verbiage; every word contributes to understanding the tool's purpose and context 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 adequate for basic use but incomplete. It lacks details on output (e.g., boolean result or error messages) and edge cases, which are important for a mathematical tool. The domain/category tags help, but more behavioral context would improve completeness.

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, but the description adds crucial semantics: it explains that 'p' must be a prime number and defines the Sophie Germain prime condition (2p + 1 is also prime). This compensates well for the lack of schema descriptions, providing clear meaning beyond the schema's type information.

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 p is a Sophie Germain prime (2p + 1 is also prime).' It includes a specific verb ('Check'), resource ('prime p'), and mathematical definition, clearly distinguishing it from sibling tools like 'is_prime' or 'is_safe_prime' by focusing on this specific 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 implies usage by specifying the domain ('arithmetic') and category ('special_primes'), which suggests it should be used for prime number analysis in mathematical contexts. However, it does not explicitly state when to use this tool versus alternatives like 'is_safe_prime' or other primality tests, nor does it provide exclusions or prerequisites.

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