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

Annotations already declare readOnly, idempotent, non-destructive, so safety is covered. The description adds genuinely non-obvious behavioral context: a $0.001 USDC x402 charge per successful call on Solana, an equivalent HTTPS endpoint, and the domain 1..1000000. It omits what happens on payment failure or invalid input, which keeps it short of a 5.

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 definition, then examples, then the valid domain, then the payment/transport details. Four compact sentences, each of which conveys new information an agent would otherwise have to guess.

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?

There is no output schema, but the worked examples effectively communicate the return value and its type. Combined with the payment and rate/endpoint information, an agent has enough to call it correctly; only error/failure semantics are absent.

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% and the single parameter is undocumented in the schema, so the description must carry the load. It does so reasonably: n is defined as the lower bound on the returned arithmetic number, with four input/output examples that make the mapping concrete, though the stated 1..1000000 range merely repeats the schema's min/max.

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 precise function: the smallest arithmetic number that is at least n, and backs it with worked examples (2 gives 3, 8 gives 11) that pin down the otherwise jargon-heavy term 'arithmetic number'. It does not, however, distinguish itself from the many arithmetic_* siblings (arithmetic_number, arithmetic_count, arithmetic_second), so an agent must infer the difference.

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 that n is a lower bound and the tool rounds up within the arithmetic-number sequence, which gives the agent an implicit usage model. There is no explicit when-to-use framing, no statement of when another sibling (e.g. arithmetic_number for a membership test) would be the better choice.

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