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

Annotations only declare readOnly/idempotent/openWorld=false, so they say nothing about output. The description fills that gap by disclosing the three things returned: primality, smallest factor plus full factorization, and nearest primes. It does not discuss the 1e12 cutoff behavior or performance, so it stops short of a full behavioral picture.

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 'Is 91 prime? No – it is 7 × 13' opener front-loads the core behavior vividly and the capability list follows efficiently. The trailing URL is housekeeping rather than task information, which slightly dilutes density but costs little.

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 no output schema, the description carries the return-value burden and does so, naming the three results an agent can expect from a one-parameter read-only math tool. Remaining gaps (behavior above 1e12, how 'nearest primes' is scoped) are minor for an idempotent calculator.

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% for the single parameter n (0 to 1,000,000,000,000 with a default of 97), so the schema already carries the semantics. The description's phrase 'any whole number up to one trillion' merely restates the documented bounds and adds no format detail. 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?

States specific capabilities with a concrete verb set: test any whole number's primality, see its smallest factor and prime factorization, and find the nearest primes. That breadth distinguishes it from near-neighbors like square_root_calculator, lcm_gcd_calculator, or exponent_calculator, which do not expose factor structure or nearby primes.

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 stated domain ('any whole number up to one trillion') but the description never says when to prefer this over siblings that also take a number (lcm_gcd_calculator, scientific_calculator) or what happens outside the range. There is context but no explicit when/when-not routing.

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