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

Annotations already declare readOnly, idempotent, openWorld, and non-destructive behavior. The description adds payment model (per successful call), an HTTPS endpoint, and primality/range constraints, though it does not specify error behavior for composite p or the exact return type.

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-loads the definition, immediately gives clarifying examples, then constraints, price, and endpoint in compact sentences. Every sentence earns its place with no redundancy.

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 deterministic math function with no output schema, the description supplies definition, examples, domain constraints, pricing, and endpoint. It stops short of explicitly stating that the return value is a non-negative integer and what happens on invalid input, which keeps it from a 5.

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 compensate. It defines both parameters meaningfully: n as bounded 1..1000000000000 and p as requiring a prime, adding a primality constraint beyond the schema's integer bounds; only p's upper bound is left to the 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?

States a specific mathematical operation (p-adic valuation v_p(n)) and clarifies it as 'how many times the prime p divides n,' with clear examples for p=2,3,5 on n=12. An agent can distinguish this from sibling prime/factorization tools without opening any schema.

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?

Provides concrete usage conditions: p must be prime, n runs from 1 to 1000000000000, and each successful call costs $0.001 USDC via x402 on Solana. It does not name alternatives or explicitly state when not to use it, but the domain constraints are clear.

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