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

No annotations, so the description carries full burden. It usefully discloses an input constraint (rejects values above 2^53-1) and the payment model (5 free trial calls per signed wallet), but says nothing about the return shape (presumably a boolean) or behavior on edge 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?

A single front-loaded sentence covering the operation, the optional base, and the upper-bound constraint, with the pricing note appended. Efficient, though the emoji/trial-call marketing text is noise for tool selection.

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?

No output schema, no annotations, and no schema descriptions mean the description is the only source of truth. It covers the core semantics and one constraint, but omits return format and the practical difference from sibling primality tools, leaving gaps an agent would need.

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% for both params, so the description must compensate. It adds real value for 'base' (default 2, Fermat base) and implies 'value' is a numeric magnitude via the 2^53-1 limit, but never states that both are passed as strings or what formats are accepted.

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 value is prime or a Fermat pseudoprime to base a'. The inclusion of the base parameter distinguishes it from the sibling x402-is-prime, though the 'prime or pseudoprime' phrasing slightly blurs the boundary with strict primality tests.

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?

No guidance on when to choose this over x402-is-prime, x402-is-fermat, x402-miller-rabin, or the other primality siblings. The default base=2 is the only hint about intended use; there is no explicit when/when-not.

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