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

Beyond the readOnly/idempotent annotations, the description discloses two things an agent cannot get anywhere else: output type changes to a decimal string past 15 digits (a real serialization surprise), and the call costs $0.001 USDC via x402 on Solana with a same-tool HTTPS mirror. Cost and format-shift disclosure are exactly the behavioral facts that prevent bad agent decisions.

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 definition is front-loaded in the first clause, followed by examples, bounds, format caveat, price, and endpoint — each sentence carries distinct, non-redundant information. No filler and no repetition of the schema.

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 still tells the agent the result type flips to a string past 15 digits, which is the main return-value hazard for a bignum tool. Range, pricing, and an alternate transport are all covered, leaving nothing an agent needs in order to call this correctly.

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 description carries the burden, and it does: it explains that n is the exponent, bounds it to 1–128, and gives three concrete n→value pairs that let an agent sanity-check interpretation. It stops short of stating what happens at out-of-range n, which the schema's minimum/maximum already constrain.

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 first sentence states the exact mathematical resource and operation (2^n - 1), which is unambiguous and self-verifying via the worked examples (n=1→1, 2→3, 31→2147483647). It does not explicitly distinguish itself from the sibling mersenne_prime, so an agent must infer the value-vs-primality split from the names alone.

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 range 'n runs from 1 to 128' and the three worked examples imply usage clearly enough that an agent can call it correctly. However, there is no explicit when-to-use statement or routing to alternatives such as mersenne_prime, so usage is inferred rather than stated.

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