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

Annotations already declare the safety profile: read-only, idempotent, non-destructive, and open-world. The description adds useful operational context beyond annotations, including the per-call price, x402/Solana payment mechanism, and an equivalent HTTPS 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 description is front-loaded with the core behavior and examples, followed by the valid range and payment details. It is appropriately concise, though the examples and endpoint details add some length.

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 one-parameter mathematical counting tool with no output schema, the description gives enough to call it correctly: the meaning of n, its range, and sample counts at specific thresholds. It does not formally define a Blum integer, but the examples and sibling family make the intent sufficiently clear.

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 the parameter explanation. It does so reasonably well: n is presented as the upper bound ('at most n') and its valid range is stated as 1 to 5000, matching the schema 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 clearly states a specific operation: counting Blum integers at most n, with concrete examples. It is easy to distinguish from generic math tools, but it does not explicitly differentiate itself from close siblings such as blum, blum_factors, blum_next, or blum_sum.

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 question-style phrasing and the boundary examples. However, there is no explicit guidance on when to use this tool instead of the closely named Blum-related siblings, and no when-not guidance is provided.

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