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

No annotations are provided, so the description carries the full behavioral burden, and it discloses nothing: not the boolean nature of the result, not the mathematical precondition that p be prime and g coprime to p, not what happens on invalid input.

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?

Very short, but shortness is not conciseness here — the single sentence is a pure duplicate of the title and earns no place. There is no front-loaded statement of purpose or result.

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 mathematical predicate tool with no annotations, no output schema, and two undescribed parameters, the description leaves an agent without the essential facts: whether the return is a boolean, and the number-theoretic constraints on g and p. It is completely inadequate.

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 of 3 applies by the stated rule. The caveat is that the schema text itself is vacuous ('G to process', 'P to process'), and the description contributes nothing beyond it, so it sits at the bottom of the baseline rather than above it.

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 'Is Primitive Root: Is Primitive Root' simply restates the tool name verbatim, which is the definition of a tautology. While the name is domain-specific enough to hint at a number-theory predicate, the description adds no scope, no return semantics, and no differentiation from the many other 'is-*' predicate siblings.

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 statement of when to use this tool, no prerequisites (e.g., that p should be prime), and no mention of alternatives such as x402-prime, x402-prime-factors, or x402-multiplicative-inverse. The agent receives no routing guidance at all.

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