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

Annotations already cover the safety profile (readOnlyHint, idempotentHint, destructiveHint=false), so the bar is lower. The description adds genuinely useful context beyond them: the $0.001 USDC cost per successful call, the x402/Solana payment mechanism, and an equivalent HTTPS endpoint — material facts an agent must know before invoking.

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 with the core predicate and its domain, then appends pricing and endpoint in a single trailing sentence. Every clause is informative and nothing is repeated from the schema or annotations.

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?

The tool is a simple single-parameter predicate with no output schema, so no return-value documentation is strictly required, and payment/transport details are present. However, the underlying notion of a 'Higgs prime for exponent 2' is obscure and is only conveyed through examples, and the boolean response shape is implied rather than stated.

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 semantics, and it does: it defines what n represents, gives the valid domain 1–2000, and supplies concrete in/out examples that pin down the predicate's meaning. It does not explain what happens for out-of-range values, but the core semantics are covered.

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 predicate: whether integer n is a Higgs prime for exponent 2, and backs it with worked examples (2, 13, 19 yes; 4, 9, 17 no). It is clearly a membership test rather than a sequence generator, so an agent can distinguish it from higgs_next/higgs_index even though those siblings are never named.

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 constraint ('n runs from 1 to 2000') and the positive/negative examples imply when the tool applies, but there is no explicit routing guidance such as 'use higgs_next to enumerate the next Higgs prime' or 'use higgs_count for a count in a range'. Usage is inferable but not stated.

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