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 useful context beyond them: a per-call price of $0.001 USDC via x402 on Solana, charged only on successful calls, and a direct HTTPS endpoint. It stops short of saying what the response body looks like.

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 leads, followed by examples, domain, pricing and endpoint — a sensible front-loading with no filler sentences. The opening 'Whether n is prime...' is a sentence fragment, a minor structural blemish.

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 predicate with no output schema, the description covers semantics, valid domain, cost and transport, which is nearly everything an agent needs. The remaining gap is the return shape (a bare boolean vs. a structured verdict), which is not stated anywhere.

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, and it does: it states n is the integer under test and constrains it to 1–10000. That is adequate for a single scalar parameter, though it adds little the schema's minimum/maximum does not already encode.

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 gives a precise mathematical predicate ('n is prime and n+2 is either prime or a product of two primes, counted with multiplicity') plus worked examples (2, 41, 47 are; 43 is not), which tells an agent exactly what the tool tests. It does not name the nearest siblings (twin_prime, sophie_germain, prime_check) that overlap conceptually, so differentiation is implicit rather than explicit.

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 only implied by the definition and the 'n runs from 1 to 10000' bound; there is no statement of when to prefer this over twin_prime or sophie_germain, nor any exclusion. The HTTPS/x402 notes describe alternate access to the same tool, not alternative tools.

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