MCP Math Server

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

With no annotations provided, the description carries the full burden of behavioral disclosure. It states the test is 'probabilistic' and for 'cryptographic applications,' which hints at reliability and use cases, but doesn't explain error rates, performance characteristics, or what 'probabilistic' entails (e.g., confidence levels based on parameter 'k'). This leaves significant gaps for a tool with potential cryptographic implications.

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 with the core purpose in the first phrase. The additional context about industry standards and domain is brief and relevant. However, it could be more structured by explicitly separating purpose from usage notes.

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 of a probabilistic primality test, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks details on parameters, behavioral traits (e.g., accuracy, speed), and output format, making it inadequate for informed tool selection and invocation.

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 description coverage is 0%, so the description must compensate. It mentions 'Miller-Rabin probabilistic primality test' but doesn't explain parameters 'n' (the number to test) or 'k' (the number of iterations/confidence parameter). Without this, users must infer parameter meanings from the tool name alone, which is insufficient for effective use.

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 performs a 'Miller-Rabin probabilistic primality test' and mentions it's an 'industry standard for cryptographic applications.' It specifies the mathematical operation (primality test) and domain context, though it doesn't explicitly differentiate from sibling tools like 'aks_primality_test' or 'deterministic_miller_rabin' beyond the 'probabilistic' qualifier.

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 (cryptographic applications) but doesn't specify scenarios where probabilistic testing is preferred over deterministic methods or other primality tests available in the sibling list, such as 'aks_primality_test' or 'fermat_primality_test'.

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