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

With no annotations provided, the description carries the full disclosure burden, and it only covers the mathematical predicate. Nothing is said about the return value (presumably a boolean), what happens for non-integer or out-of-range inputs, or how the number is supplied given the empty input schema. 'Provide value' hints that an input is required but discloses no mechanism for delivering it.

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 text is short, but the leading 'Is Giuga:' simply restates the tool name and the closing 'Provide value' dangles cryptically. The definition is packed tightly, though the notation 'n/k-1' is ambiguous as written and could be misread as n/(k-1) rather than (n/k)-1.

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 tool with an empty input schema and no output schema, everything rests on the description, and it omits the two things an agent needs: how to pass the number and what the result looks like. The mathematical definition is included but imprecise, so even the core semantics are slightly off.

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?

The schema has zero parameters, so the baseline is 4, but the description's 'Provide value' implies a parameter the schema does not define, leaving an agent unable to construct a valid invocation. The description does add meaning about what the value represents (a number to test) and the Giuga definition, but it fails to specify where or how that value is passed.

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: 'Check whether a number is a Giuga number', which distinguishes it from the many sibling is-X tools by naming the exact property being tested. Including the definition ('composite where prime factors divide n/k-1') helps an agent recognize what counts as a Giuga number. It is slightly muddied by the tautological 'Is Giuga:' opener and the cryptic 'Provide value' fragment, but the core purpose is unambiguous.

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?

There is no guidance about when to use this tool versus the hundreds of sibling predicates (is-armstrong, is-carmichael, is-smith, etc.). No exclusions, alternatives, or preconditions are given, such as noting it applies to composite candidates or that other tools test related primality properties. The only usage signal comes from the tool name itself.

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