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

With no annotations, the description carries the full burden, and it does disclose the output semantics (true for primes, false for composite or <2) explicitly, which is genuinely useful. It omits error behavior when no argument is supplied and what happens after the 5 free trial calls are exhausted beyond the terse wallet note.

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 purpose and return semantics are front-loaded in the first two sentences with no filler. The trailing emoji quota line is mildly promotional but still carries pricing information.

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 four-parameter tool with no annotations and no output schema, the description does the important work of explaining the boolean return and the <2 edge case. It falls short on resolving which of the four optional string fields to use and on any failure or billing behavior.

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 0%, so the description must compensate; it partially does by declaring n and number as interchangeable aliases for the input. It never mentions the input and value properties, which are equally plausible aliases, and never states that all values are strings, leaving the agent to guess which of the four optional fields to populate.

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: 'Check whether a number is prime', which an agent can immediately classify as a boolean predicate. It does not distinguish itself from near-siblings such as x402-prime, x402-is-prime-pair, or x402-is-twin-prime, which is the only thing keeping it from 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?

There is no guidance on when to pick this over x402-prime or the various prime-related siblings, and no stated preconditions or exclusions. The only instruction, 'Provide n or number', is parameter usage rather than tool selection guidance.

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