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

No annotations, so the description carries full burden. It usefully discloses a behavioral trait the structured data lacks — '5 free trial calls per signed wallet', i.e. rate/payment context — plus the semantic nuance about differing by two. However it never states the return shape, behavior on non-integer/non-numeric input, or what happens when the trial quota is exhausted.

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?

A single tight sentence with the purpose front-loaded, followed by a short trial note. The emoji and pricing tag add minor noise but no sentence is wasted.

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 simple two-parameter predicate with no output schema, the description covers purpose and input meaning adequately, but omits the expected boolean result and edge-case behavior, and leaves the string-vs-integer parameter type unexplained.

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% and the two parameters are only named 'a' and 'b'. The description partially compensates by tying them to 'both integers', but does not resolve the mismatch with the schema declaring them as strings, nor give formats or bounds (negative, large numbers).

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?

States a specific verb and resource ('Checks whether both integers a and b are prime') and explicitly disambiguates from the closest sibling by noting 'the pair need not differ by two', which separates it from x402-is-twin-prime-pair. An agent can select it without opening either schema.

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?

Usage is implied by the primality-check semantics and the twin-prime disambiguation hints at when this rather than that variant applies, but no alternative tool is named and no conditions for when-not-to-use are given. Minimum-viable context only.

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