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

With no annotations, the description carries the full burden and does disclose return semantics: true for primes with concrete examples (2, 3, 5) and explicit false handling for composite numbers and values below 2. It omits input-format requirements (the schema types are strings) and any note about large-number behavior.

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?

Two tight sentences, front-loaded with the operation and then the parameter/output contract. Minimal waste, though the leading 'Is Prime:' mildly restates the tool name.

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 trivial no-annotation, no-output-schema predicate with four aliased string parameters, the description covers purpose, parameter choice, and the full true/false outcome including edge cases. Only the input format (string-encoded integer) and behavior on non-numeric input are left unspecified.

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 coverage is nominally 100%, but the schema descriptions are throwaway ('N to process', 'Input to process'), so the baseline is 3. The description adds value by indicating n/number are the accepted aliases for the value to test, yet it ignores the other two aliases (input, value) and never clarifies that the number should be supplied as a string.

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?

Names a specific verb+resource ('Check whether a number is prime') and even defines the output domain (true for primes, false for composite or <2). It does not, however, explicitly differentiate itself from the many related siblings (x402-prime, x402-prime-series, x402-prime-factors, x402-is-twin-prime), so it stops short of a 5.

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 sentence 'Provide n or number' tells the agent how to call it, but there is no guidance on when to choose this predicate over the sibling prime tools, nor any prerequisites or exclusions. Usage context is essentially absent.

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