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

Annotations already cover readOnly/idempotent/non-destructive, and the description adds genuinely non-obvious operational context: a per-call x402 price of $0.001 USDC on Solana and an equivalent HTTPS endpoint. That payment/auth detail is exactly the kind of behavior annotations cannot convey. It does not state the return type explicitly, 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, followed by minimal discriminating examples, then payment/endpoint facts. Slightly duplicative (the range restated from the schema), but no sentence is wasted for a paid API tool.

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?

No output schema exists, so the description carries the burden of stating the return value — a boolean is only implied by the word 'Whether'. Combined with the undefined T(n) formula, an agent knows how to call it but not fully what it is computing; the pricing/endpoint info is a helpful partial offset.

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?

There is one parameter at 0% schema description coverage; the schema already enforces 0..30 so the description's 'n runs from 0 to 30' merely repeats the constraint. The description does establish n as an index into the T sequence, but never says what T(n) is defined as, leaving the most important semantic gap open.

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: returns whether T(n) is prime, with concrete worked examples (T(2), T(3), T(4) prime; T(0), T(1), T(5), T(6) not). It never defines what the trinomial sequence T is or points to the sibling trinomial_term, so the agent must infer the sequence from context, but the operation itself is unambiguous.

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?

Usage is only implied — you call it when you need a primality decision on a trinomial number. No when-not conditions, no mention of the related siblings (trinomial_term for the value, trinomial_sum, trinomial_mod) that an agent would plausibly want instead or alongside.

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