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

Annotations already declare readOnlyHint=true, idempotentHint=true, destructiveHint=false, and openWorldHint=true. The description adds useful context beyond annotations: the input domain, pricing model ($0.001 USDC per successful call via x402 on Solana), and an alternate HTTPS endpoint. It does not cover failure modes or payment prerequisites in detail.

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 useful examples, domain bounds, pricing, and an alternate endpoint. The range statement partially duplicates the schema, but the examples and payment details are relevant and there is little wasted text.

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 one-parameter arithmetic tool with no output schema, the description provides the definition, boundary examples, valid input range, and pricing/endpoint information. It could explicitly say the return value is an integer prime, but the examples make the return behavior clear enough.

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 supplies the inclusive domain (0 to 10,000,000) and concrete mapping examples such as 0, 1, and 2 yielding 2, and 14 yielding 17, which clarify boundary behavior beyond the schema's type and min/max constraints.

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 mathematical operation: the least prime greater than or equal to n, with concrete examples. This operation is inherently distinguishable from siblings like prev_prime, prime_nth, prime_check, and prime_count even though no sibling is explicitly named.

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 precise mathematical definition and examples, but there is no explicit guidance on when to use this tool versus alternatives such as prev_prime or prime_check. No when-not conditions or alternative routing are provided.

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