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 meaningful behavioral context: pricing per successful call, x402/Solana payment, and an HTTPS alternative endpoint.

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 purpose is front-loaded, and the examples, range, price, and HTTPS endpoint are all relevant. It is somewhat dense but not wasteful for a paid API 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 one-parameter mathematical count with annotations and no output schema, the description is nearly complete: it gives scope, range, examples, pricing, and endpoint. It could be improved by explicitly stating the integer return value and distinguishing this from sibling Pierpont 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?

Schema description coverage is 0%, so the description must carry parameter meaning. It does explain that n is the upper bound and repeats the 1..1000000 range already in the schema, and it adds useful worked examples, but it does not define Pierpont primes or clarify the return type beyond the phrase 'how many'.

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 specific verb-resource pairing: it counts Pierpont primes at most n. The examples and n bound make the operation clear, though it does not explicitly contrast itself with siblings such as pierpont, pierpont_prime, or pierpont_next.

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 counting formulation and examples, and the valid n range is stated. However, there is no explicit guidance on when to choose this tool instead of the related Pierpont tools, nor any when-not-to-use conditions.

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