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

Annotations already declare readOnlyHint, idempotentHint, destructiveHint=false and openWorldHint, so the safety profile is covered. The description adds genuinely non-structured context: the cost ($0.001 USDC per successful call via x402 on Solana) and an alternate HTTPS endpoint — material facts an agent needs before invoking a paid 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?

Definition and examples come first, then domain, then payment and endpoint — three short sentences with no filler. Every clause carries distinct information.

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 single-integer pure function with no output schema, the definition plus examples fully specify the return value, and the domain and cost are disclosed. The only shortfall is the absence of any pointer to related siblings like little_omega for an agent choosing among near-identical factoring tools.

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?

Only one parameter and schema coverage is 0%, but the schema itself carries min/max bounds and the description's range statement duplicates rather than extends them. The description implicitly defines n as the integer being factored, which is useful, but adds little beyond the schema's type and bounds.

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 the exact mathematical object ('number of prime factors of n counted with multiplicity') plus three worked examples (Omega(1)=0, Omega(4)=2, Omega(12)=3) that pin down the difference between this and a distinct-prime-factor count. An agent can distinguish it from the sibling little_omega purely from the description.

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 and domain constraint ('n runs from 1 to 1000000000000') imply when the tool applies, but it never explicitly contrasts itself with little_omega or any other factoring sibling, and offers no when-not guidance. Usage is inferable rather than stated.

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