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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive), so the bar is lower. The description adds genuinely useful non-schema context: a price ($0.001 USDC per successful call via x402 on Solana) and an alternate HTTPS endpoint, which an agent needs to know before incurring cost.

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?

Front-loaded with the core purpose, then examples, then constraints and pricing. The examples are somewhat verbose but serve as return-value illustration in the absence of an output schema, so they earn their place.

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 single-parameter pure-math tool with no output schema, the description conveys the result shape through concrete examples (e.g. n=11 only n!+1 prime) and includes cost/endpoint details. Only gap is the exact return structure (field names/types) not being spelled out.

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 must carry the load. It does so by stating the valid range (n runs from 0 to 12) and flagging the n=0/1 edge case for n!-1, adding behavioral meaning beyond the raw minimum/maximum in the schema.

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, unambiguous purpose: testing primality of n!+1 and n!-1. The verb/resource pair is clear and the worked examples pin down the semantics, though it never explicitly contrasts with near siblings like factorial_mod, primorial_prime or wilson_prime.

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?

It gives the domain constraint (n from 0 to 12) and worked examples of expected output, which implicitly tells an agent when the tool applies. However, there is no explicit statement of when to choose this over the many related factorial/prime siblings.

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