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

Annotations already cover the safety profile (readOnlyHint=true, idempotentHint=true, destructiveHint=false, openWorldHint=false), so the description focusing on the deterministic Miller-Rabin base set and the two-tier factorization limits adds genuinely useful behavioral context about correctness guarantees and computational ceilings.

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?

A single dense sentence that front-loads the main capability and then appends the secondary factorization behavior. Nothing is wasted, though the parenthetical bounds are somewhat heavy for the space.

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?

With an output schema present, the description need not explain return values, and it supplies the algorithm and limit details needed to know when the result is trustworthy. Only the lack of guidance on edge cases (e.g. 0 or 1) keeps it from a 5.

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%, and the schema already documents the 0 <= n < 3.3e24 range, the 25-digit cap, and the factorization limits. The description largely restates those same bounds, so it adds little beyond the schema; baseline 3 applies.

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 (Compute) and resource (deterministic primality / factorization) with precise numerical bounds and algorithm details. It is not tautological, but it never differentiates itself from math siblings like gcf_calculator or simplify_sqrt.

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 explicit when-to-use or when-not, and no alternative tools are named. Usage is only implied by the tool's nature (check if a number is prime, or factor it), which is adequate for a self-contained calculator but leaves the agent to infer the boundaries.

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