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

Annotations already establish readOnly, idempotent, non-destructive, open-world behavior, so the bar is lower; the description nevertheless adds genuinely non-obvious context: the call is paid ($0.001 USDC via x402 on Solana) and an equivalent HTTPS/JSON endpoint exists. It also pre-discloses the answer for every legal input, which is useful for a cached-lookup style tool.

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 answer semantics, then the domain, then the enumeration of results, then payment and transport details. Every sentence is short and carries distinct information; nothing is repeated from the schema or annotations.

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-parameter boolean lookup with no output schema, the description covers results by example but never states the return type (boolean), the error behavior for invalid n, or what an 'alternating factorial' is for an agent that needs to justify the answer. Adequate but with obvious gaps.

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% for the single parameter n, so the description has to carry meaning. It states 'n runs from 1 to 12', which duplicates the schema's minimum/maximum rather than explaining that n is the index into the alternating-factorial sequence, and it never says what happens for 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?

The description states a specific predicate over a specific mathematical object: whether the alternating factorial a(n) is prime. That is clear enough to distinguish it from computational siblings such as alternating_factorial or alternating_sum, though it never names an alternative directly and assumes the reader knows what 'alternating factorial' means.

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?

There is no statement of when to use this tool rather than alternating_factorial (which computes a(n)) or prime_check. The list of which n yield true/false reads as documented results, not as guidance on selecting or invoking the tool, so the agent must infer usage from the domain alone.

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