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

Adds real behavioral context beyond the annotations: the call is metered at $0.001 USDC per successful call via x402 on Solana, plus an alternate HTTPS endpoint. That tells the agent about cost and payment preconditions, which the readOnly/idempotent annotations do not cover. It does not describe failure or refund behavior.

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?

Four short sentences, zero waste, and front-loaded with the definition before examples, domain, and access details. Every sentence adds information an agent would otherwise have to guess.

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 pure function with no output schema, the definition, examples, domain, price and endpoint cover nearly everything needed to invoke it. The only gap is not stating the return value explicitly, though the examples imply it.

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 coverage is 0%, so the description carries the burden: it gives the valid domain (1 to 10000) and four input→output examples that define what 'at least n' means for the single parameter. Only missing piece is an explicit statement that the response is the integer itself.

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 verb+resource: 'the smallest Blum integer that is at least n', with worked examples (1→21, 22→33) that make the 'next' semantics unambiguous. It does not name a sibling, but the lower-bound phrasing clearly separates it from blum, blum_count, blum_factors and 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 domain statement 'n runs from 1 to 10000' rather than stated as guidance. There is no explicit 'use this instead of X' routing or exclusion, which matters in a family of four Blum tools.

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