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

With no annotations, the description carries the full behavioral burden. It usefully discloses domain boundaries beyond the schema — the supported range and that prime status is only defined for n >= 2 — which is genuinely additive. But it is silent on what happens for out-of-range inputs or n < 2 (e.g., is 1 prime? error?), and says nothing about performance for large composites.

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?

Two tight sentences with zero waste. The core capability is front-loaded, and the domain constraint follows immediately as supporting detail.

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?

There is no output schema, so the description must carry return-value semantics — and it only partially does. It says it returns the prime factorization, but leaves ambiguous what is returned for composite inputs, for n < 2, or for out-of-range values. Adequate for the core case but with a real gap for a tool whose output shape is undocumented.

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% with a single integer parameter, so the schema already fully documents the accepted range. The description merely restates that range, adding no syntax or format detail beyond structured data. Baseline 3 applies when the schema does the heavy lifting.

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+resource: 'Check whether an integer is prime and return its prime factorization.' An agent immediately knows this is a primality test plus factorization tool. The sibling tools (common_base_multiply, generate_java_algorithm) are unrelated, so no differentiation is needed.

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?

Usage is implied by the description ('check whether an integer is prime'), and the domain constraints (range -10^12 to 10^12, prime status only for n >= 2) effectively define when the tool is applicable. However, there is no explicit when-to-use or when-not-to-use guidance and no alternatives to route to, since the siblings are unrelated.

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