MCP Math Server

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 counts primes up to n, but does not disclose behavioral traits such as performance characteristics (e.g., handling large n), error handling, or output format. 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 highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and mathematical function, followed by domain/category tags. Every word earns its place with no redundancy or unnecessary elaboration.

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 (one parameter, no output schema, no annotations), the description is minimally complete. It explains what the tool does and the parameter's role, but lacks details on output format, limitations, or error cases, which are needed for full contextual understanding.

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 description adds significant meaning beyond the input schema, which has 0% coverage. It explains that parameter 'n' is the upper bound for counting primes (less than or equal to n), clarifying its role in the prime counting function. With only one parameter, this provides sufficient semantic context.

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 with a specific verb ('Count') and resource ('prime numbers'), explicitly defines the mathematical function (prime counting function π(n)), and distinguishes it from sibling tools like 'is_prime' or 'first_n_primes' by focusing on counting rather than testing or listing primes.

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 and category, but does not specify use cases, prerequisites, or compare it to sibling tools like 'prime_counting_sieve' or 'prime_density_analysis', leaving the agent without contextual usage direction.

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