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

Annotations already cover read-only, idempotent, non-destructive semantics, but the description adds real behavioral context the schema does not carry: even inputs are rejected, the cost is $0.001 USDC per successful call via x402 on Solana, and an equivalent HTTPS endpoint exists. Payment/auth cost disclosure is exactly the kind of thing an agent needs before invoking. It stops short of describing the response shape.

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?

Compact overall, but the lead-in buries the operation behind a mathematical definition and examples. The worked examples (1, 3, 127, 905) consume space without clarifying what the call returns; the pricing/endpoint tail is useful and appropriately last.

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 single-parameter paid predicate tool with no output schema, the description should say what the return value is (boolean membership? sequence term?). The domain constraints and pricing are covered, but the missing result contract is a meaningful gap an agent must resolve by inference.

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 carry parameter meaning. It adds the important 'even n is rejected' constraint not present in the schema, and restates the 1–100000 range (already in schema). It does not clarify that n is the integer being tested for the de Polignac property, leaving the core semantic implied.

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 defines the de Polignac concept and gives worked examples (1 qualifies, 3 does not, 127 and 905 are members), which signals this is a membership test for odd n. However, it never states the actual operation or result type — 'whether...' implies a boolean but the tool could plausibly return a representation count or a listing. An agent can guess the subject matter but not with certainty what comes back.

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 use this versus the many adjacent number-theory siblings (goldbach, odd_goldbach, prime_check, etc.), and no exclusions beyond the 'even n is rejected' domain constraint. The one domain restriction mentioned is a parameter validity rule, not usage guidance.

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