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

Annotations already cover readOnly, idempotent, openWorld and non-destructive, so the safety bar is low; the description still adds valuable non-schema behavior: a hard domain of 1 to 1e12, a per-successful-call price of $0.001 USDC via x402 on Solana, and an equivalent HTTPS endpoint. It does not state the response shape (presumably a boolean) despite there being no output schema, which is the main remaining gap.

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 core definition is front-loaded, followed by confirming examples and then domain/cost/endpoint logistics — every element serves a purpose. The three example sentences are slightly more illustrative than strictly necessary, but they genuinely reduce misinterpretation of the predicate.

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 one-integer predicate tool, the description covers definition, domain, cost and an alternate transport, which is more than most siblings in this set. The only material omission is the return type, which an agent must infer from the phrasing 'Whether ...' since no output schema exists.

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 parameter meaning — and it does: n is the integer being tested, defined by the predicate itself and bounded to 1..1000000000000. The range restates the schema's min/max, so the added value is mostly the semantic definition of n rather than new format details.

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 gives a precise mathematical predicate — n and (n-1)/2 both prime — with worked positive examples (5, 7, 23) and negative examples (3, 17), so an agent can tell this apart from a generic prime_check. It does not name the nearest sibling, sophie_germain (a closely related but distinct concept), so the differentiation is by definition rather than by reference.

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 implied by the definition: call it when you need to test whether n is a safeprime. There is no explicit statement of when not to use it, no pointing to prime_check or sophie_germain as alternatives, and no note on how to handle out-of-range inputs. The pricing/endpoint line adds practical context but not selection guidance.

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