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

Annotations already declare readOnly, idempotent, openWorld, and non-destructive behavior. The description adds valuable context beyond annotations: the exact return semantics (prime and exponent, or 0), the supported input range, and the pricing model ($0.001 USDC per successful call via x402 on Solana). It also provides an HTTPS endpoint for direct access.

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 description is front-loaded with the core conditional behavior, then examples, then range and pricing. It is reasonably efficient, though the range is repeated from the schema and the pricing/endpoint sentence, while useful, is somewhat orthogonal to the mathematical operation.

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 explains the return values (prime and exponent, or 0). Annotations cover the safety profile, and the description covers input range, examples, pricing, and endpoint. It is nearly complete for a simple mathematical predicate tool, though it could mention behavior for invalid inputs (e.g., n<1 or n>1e12).

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 must carry the burden for the single parameter n. It states the valid range (1 to 1,000,000,000,000) and gives examples of n values (8, 49, 12), which helps ground the parameter's meaning. However, it does not describe edge cases, type constraints, or error behavior beyond the range.

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 conditional behavior: if n is a prime power p^k with k>=1, return the prime and exponent; otherwise return 0. It includes concrete examples (8=2^3, 49=7^2, 12 is not). However, it does not explicitly differentiate this tool from closely related siblings such as prime_check, perfect_power, or prime_nth.

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 description gives an example of a non-prime-power input ('12 is not a prime power'), which implicitly indicates when the tool returns 0. But it offers no explicit guidance on when to use this tool versus alternatives like prime_check or perfect_power, and there are many sibling tools with overlapping mathematical domains.

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