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: no return semantics, no edge cases (e.g., negative or zero input), no error behavior. It is essentially opaque.

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 text is extremely short, but this is under-specification rather than conciseness; it contains no load-bearing information. A single duplicated fragment is not an efficient structure.

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 one-parameter predicate tool with no annotations and no output schema, the description should at minimum state the domain of the check and the expected result. It communicates none of this, leaving the agent with nothing beyond a cryptic name.

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%, so the single 'value' parameter is documented in the schema (albeit generically as 'Value to process'). Per the rubric, full schema coverage establishes a baseline of 3 even when the description adds no parameter detail.

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 Woodall: Is Woodall' merely restates the tool name and title, offering no verb-plus-resource statement of what it actually does. An agent cannot tell from the text that this presumably tests whether a number is a Woodall number (n·2^n − 1) rather than some other predicate.

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 indication of when to use this tool, what input it expects, or how it relates to sibling predicates like x402-is-prime or x402-is-mersenne. No alternatives or conditions are named.

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