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

Annotations already declare readOnly, idempotent, non-destructive behavior; the description adds domain range, partner definition, pricing ($0.001 USDC per successful call), and an HTTPS endpoint. It still does not explicitly describe the return shape or out-of-range behavior, though 'Whether' implies a boolean.

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?

Front-loaded with the core predicate and examples, then constraints and payment info. 'The partner is n+2' repeats the first sentence, a minor redundancy, but overall the description is compact and structured.

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 simple one-parameter predicate with annotations covering safety, the description supplies the mathematical meaning, range, examples, and access details. The main missing piece is an explicit statement that the output is boolean; otherwise it is complete enough to invoke 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 coverage is 0% for the single n parameter, but the description compensates by stating n's range (1 to 10^12), that the partner is n+2, and giving examples such as 3→5 and 5→7. The integer type is only in schema, but the mathematical semantics are clear.

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 precise predicate: whether n and n+2 are both prime, with concrete examples distinguishing twin pairs from non-pairs. It does not name alternatives like cousin_prime or sexy_prime, so sibling differentiation is implicit rather than explicit.

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 definition implies the tool is for testing twin primality and gives a clear example, but it does not state when to choose it over prime_check, cousin_prime, or sexy_prime. No exclusions or alternative routing are provided.

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