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

Annotations already declare readOnly, idempotent, non-destructive, open-world, so the safety profile is covered. The description adds context beyond them: the input domain (n from 1 to 1000000), the paid x402/Solana cost per successful call, and an equivalent HTTPS endpoint - all operationally relevant details not in the annotations.

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?

Definition comes first, then examples, then range and pricing/transport - a sensible front-loaded order with no filler. The pricing/HTTPS sentence is boilerplate but genuinely relevant for an x402 paid 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?

For a one-integer predicate tool with no output schema and full annotation coverage, the description is nearly complete: it defines the property, bounds the domain, and discloses cost. Missing only an explicit statement of the return type (predicate/boolean) and what happens outside 1..1000000.

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 description coverage is 0%, but the single parameter is trivially named and its constraints (min 1, max 1000000) are already encoded in the schema. The description repeats the same range and defines n only implicitly through 'no cube divides n', adding little syntax or edge-case guidance (e.g., behavior for n=1 or out-of-range input).

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 predicate (no cube divides n) with four positive and four negative worked examples, so the agent can distinguish it from cubefull, squarefree, and cubefree_count without inspecting the schema. Verb/resource is precise for a math predicate tool.

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 examples imply when the tool is appropriate (single-number membership test), but there is no explicit statement of when to prefer cubefree over cubefree_count, cubefull, or squarefree. The alternatives exist as siblings and are never referenced.

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