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

Annotations already declare readOnly/idempotent/non-destructive, so the bar is lower, yet the description still adds substantive context: the 20-step / 12-digit chain limit that causes rejection, and the per-call cost ($0.001 USDC via x402 on Solana) with an alternate HTTPS endpoint. The only gap is not stating what a rejected call returns (error versus sentinel value).

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 definition and examples are front-loaded in two short sentences, followed by constraints and billing in a compact tail. Every sentence carries information; the pricing/URL sentence is operationally relevant rather than filler.

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?

A single-parameter, no-output-schema tool is fully specified: input range, counting convention, failure conditions, and cost are all present. Only the exact rejection behavior (error shape) and any mention of the sibling home-prime tools are missing, which are minor for this domain.

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 load, and it does: 'n runs from 2 to 10000' plus four worked examples that pin down what n denotes and how the step count is defined for different inputs. The bounds themselves duplicate the schema's minimum/maximum, but the worked examples add real semantic value.

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 names a specific computed quantity — how many factor-concatenations turn n into a prime — and grounds it with concrete examples (2 takes 0, 4 takes 2, 10 and 16 take 4). It distinguishes the 'step count' variant from sibling concept tools like home_prime and home_prime_len implicitly through the definition, though it never names them.

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?

The domain of n (2 to 10000) and the rejection rule (chains past 20 steps or 12 digits) tell the agent when a call is valid, and the HTTPS endpoint plus price give operational context. However, there is no guidance on when to prefer this over the neighboring home_prime / home_prime_len tools, so usage is only implied.

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