math_prime_number_checker

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

With no annotations, the description must carry the behavioral burden. It mentions operations and algorithms but fails to specify expected parameter values for 'operation' (no enum), the role of 'n' for each operation, or any side effects/rebounds. The return format and edge case handling (e.g., negative n) are absent.

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 (two sentences) and front-loads key actions. However, it includes an extraneous reference to describe_tool and lacks structured separation of operations, slightly reducing clarity.

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?

For a tool with multiple operations and two required parameters (no enums, no output schema), the description is insufficient. It does not fully specify how to invoke each operation, expected input formats, or return behavior, forcing reliance on an external describe_tool call.

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?

Schema coverage is 0%, so the description must compensate. It describes high-level operations but does not map them to specific 'operation' string values or clarify what 'n' represents in different contexts (e.g., for range listing vs. next/previous prime). This leaves ambiguity for parameter usage.

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: testing if a number is prime, listing primes in a range, and finding next/previous prime. It mentions specific algorithms (trial division, Miller-Rabin, Sieve of Eratosthenes) which further distinguishes it from sibling math tools that do not handle prime numbers.

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 via the listed operations but does not explicitly state when to use this tool over alternatives. It references 'describe_tool' for full guidance, but no direct comparisons to siblings or conditions for non-use are provided.

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