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

Annotations already declare readOnlyHint, idempotentHint, non-destructive, and openWorld behavior. The description adds useful context beyond annotations: the $0.001 USDC x402 payment model and an alternate HTTPS endpoint. It implies a boolean result via 'Whether' but does not explicitly describe the return value, keeping it from 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?

The description is front-loaded with the core definition, followed by examples, range, and payment/endpoint details. Every sentence contributes useful information, and the total length is appropriate for a simple one-parameter predicate 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 simple boolean number-theory predicate with one parameter and no output schema, the description covers the mathematical definition, examples, input range, and payment context. It could explicitly state that the tool returns true/false and address the boundary case at n=1000000, but the essential information is present.

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%, so the description must carry parameter meaning. It identifies n as the starting integer of the pair n and n+1 and states the valid range 1 to 1000000, which adds semantic context beyond the bare integer/min/max schema.

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 precisely defines the Ruth-Aaron predicate: whether n and n+1 have the same sum of prime factors counted with repetition. It includes concrete true/false examples, making the mathematical operation unambiguous and distinguishable from sibling number-theory tools.

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 predicate definition and the stated input range 1 to 1000000, but there is no explicit guidance on when to choose this tool versus related siblings such as sopfr or sopf. It lacks when-not-to-use conditions or named alternatives.

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