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

Annotations already declare the tool as read-only, idempotent, and non-destructive. The description adds useful behavioral detail: it uses trial division curious, outputs prime factors in power form, and lists divisors. This goes beyond the structured fields without contradicting them.

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 two sentences with no fluff; the primary function is front-loaded Joseph, and the algorithm and source are appended in one compact sentence. It is appropriately sized for the tool's simplicity.

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 single-parameter, read-only calculator with an output schema, the description covers the input range, the operations performed, and the output expectations. Nothing needed for correct invocation is missing.

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 coverage is 100%; the single parameter 'number' is fully described in the schema (integer, 2 to 1e15). The description repeats the same range but adds no new parameter-specific semantics beyond what the schema already documents, so baseline 3 is appropriate.

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 clearly states the tool's function: checking primality, prime factorization in power form, counting divisors, and listing them, for a specific numeric range. This distinguishes it from all sibling tools, which are calculators/converters for other domains.

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 provides clear context for when to use this tool (whenever prime-related computations are needed) and spells out the input range. It does not explicitly name alternatives, but among the many siblings none overlaps this functionality, so no exclusion is necessary.

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