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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive), yet the description adds real operational context: cost ($0.001 USDC per successful call over x402 on Solana) and an alternate transport (POST endpoint). It also flags an output quirk (values past 15 digits come back as a decimal string). The phrasing of that last note is slightly ambiguous about whether it affects the return type of this tool, keeping it from a 5.

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?

Five short, front-loaded sentences covering purpose, math property, bounds, output format and access/pricing, with no filler. Minor redundancy between the stated range and the schema's min/max, and the decimal-string sentence is slightly out of place before the access notes.

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?

With no output schema, the description carries the burden of explaining the return value, and it does: a remainder, zero when n is prime, and a decimal string when large. Combined with pricing and transport details, an agent has what it needs to call this correctly; only a more explicit statement of the exact return type/shape is missing.

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%, so the single parameter `n` depends on the description. The description supplies the valid domain (1 to 8192, matching the schema bounds) and, more valuably, the semantics tying the parameter to the primality interpretation of the result. It adds meaning beyond a bare integer property, though it does not discuss type/format expectations for the returned string case.

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 states a precise verb+resource: compute the remainder of the nth Perrin number divided by n (R(n) mod n). It also gives the mathematical property (prime n => remainder 0) and the input domain, which distinguishes it from the sibling `perrin` (which presumably returns the Perrin number itself). It does not explicitly name `perrin` as the alternative, 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?

Usage is implied by the definition of the operation and the stated range 'n runs from 1 to 8192', plus the payment/HTTPS access notes. There is no explicit when-to-use / when-not-to-use guidance and no named alternative for retrieving the raw Perrin value, which is left to the agent to infer.

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