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

No annotations are provided, so the description carries the full behavioral burden, and it discloses nothing: not the probabilistic nature of the test, not the accepted input format, not the truth value or confidence returned, not whether it can be slow for large inputs.

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?

It is short, but its brevity reflects under-specification rather than concision – the single 'Miller Rabin: Miller Rabin' string wastes its one opportunity to state purpose. Nothing is front-loaded because nothing informative is present.

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 no annotations, no output schema, and a generic 'value' parameter, the description is entirely inadequate. An agent has no basis to invoke it correctly over its numerous primality-testing siblings.

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 100% with a single 'value' parameter described as 'Value to process', so per the high-coverage baseline the schema carries the load and a 3 applies. The description itself adds nothing about expected numeric format or ranges.

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 is the tautology 'Miller Rabin: Miller Rabin' – it merely restates the tool name and adds no verb, resource, or scope. An agent cannot learn from the text what the tool returns or that it is a probabilistic primality test.

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?

There is no when-to-use guidance and no differentiation from the many adjacent primality siblings (x402-is-prime, x402-is-prime-pair, x402-is-pseudoprime, x402-is-carmichael, x402-prime-factors). The agent is left to guess whether this validates, generates, or tests primes.

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