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

Annotations already declare readOnly, idempotent, non-destructive and open-world, so the safety profile is covered. The description adds genuinely new operational context beyond the schema: a per-call price of $0.001 USDC via x402 on Solana and an equivalent HTTPS endpoint — exactly the auth/payment information an agent needs before calling.

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 is front-loaded, followed by examples, the valid input range, and then pricing/transport. Every sentence is short and useful; the four worked examples are slightly more than strictly necessary but aid disambiguation in a very crowded math-tool namespace.

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?

With no output schema, the description should say what comes back; 'whether' implies a boolean but the response shape (bare boolean vs. JSON with the neighbouring primes) is never stated. It is also unclear whether a 'not prime/balanced' answer still incurs the $0.001 charge. Adequate for calling, thin on returns and cost semantics.

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, and it does state that n is the integer under test and bounds it to 1..5000 (reinforcing the schema's min/max). It adds the meaning of the parameter, though it does not explain the behaviour outside the range or whether the bound is inclusive.

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 defines the exact predicate — prime and equal to the mean of its neighbouring primes — with worked true (5, 53, 157, 1103) and false (2, 3, 7, 11) examples, which cleanly separates it from siblings like prime_check or twin_prime. It is framed as a noun phrase ('Whether n is...') rather than a verb+resource, but an agent can tell exactly what is being computed.

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 statement ('n runs from 1 to 5000') and the true/false examples implicitly tell the agent when the tool applies and what it will answer. There is no explicit when-to-use/when-not or named alternative (e.g., prime_check for plain primality), so guidance is implied rather than stated.

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