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

With no annotations provided, the description carries the full burden of behavioral disclosure. It clearly explains the boolean return convention, including the important edge case that numbers <2 return false. It does not describe behavior for non-integer or invalid inputs, but for a simple primality check the core behavior is transparent enough.

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 description is a single, front-loaded sentence that conveys the purpose, parameter names, and return semantics with no filler. Every clause earns its place and an agent can extract the essential information quickly.

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 simple one-parameter boolean predicate with no output schema and no annotations, the description covers purpose, input aliases, return values, and the key edge case of numbers <2. It could be more complete by mentioning how invalid or non-integer inputs are handled, but this is a minor gap for a tool of this simplicity.

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 100%, so the baseline is 3. The description adds a small amount of meaning by mentioning 'number' as an accepted alternative to 'n', and implies a numeric value is expected. However, it does not clarify the type mismatch between the schema's string type and the numeric intent, nor does it specify the range or format of acceptable input.

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 verb ('Check') and a specific resource ('whether a number is prime'), and defines the exact output semantics: true for primes like 2, 3, 5 and false for composites or numbers <2. It also mentions an alternate input name ('number'), which adds flexibility. The purpose is immediately clear and distinct from the many sibling tools.

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 description implies the usage context by saying 'Check whether a number is prime' and tells the caller to provide 'n or number'. However, it does not explicitly differentiate this from related siblings such as is-prime-pair, is-twin-prime, is-mersenne-prime, or prime-factors, nor does it state when not to use this tool. It is adequate but leaves alternative-selection to inference.

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