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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive), and the description adds real context beyond them: the per-call price ($0.001 USDC via x402 on Solana) and an alternative HTTPS endpoint. That cost/payment detail materially affects whether an agent should call it.

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?

Four short, front-loaded sentences with no filler; the core semantics come first and the pricing/endpoint note comes last. The HTTPS URL is somewhat tangential to tool selection but is compact enough not to hurt readability.

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 predicate with no output schema, the description covers input validation, cost, and the modality of the answer. It stops short of stating the exact return shape (e.g., boolean field name), which is the one thing an agent would still have to discover by calling it.

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 the burden, and it does: it clarifies n is the integer under test, that 1 is not considered prime, and that n < 1 is rejected. The upper bound of 10^12 restates the schema maximum rather than adding new information, keeping it just short of a 5.

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 specific verb (test) and resource (primality of n) plus the algorithm ('by trial division'), which distinguishes it from sibling tools like next_prime, prime_count, or factor-oriented tools. An agent can tell immediately that this is a boolean primality predicate rather than a generator or counting function.

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 domain boundaries (1 is not prime, n < 1 rejected, n ≤ 10^12) but never says when to prefer this over siblings such as next_prime or largest_prime_factor. Usage is implied by the tool's semantics rather than explicitly routed.

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