sieve_of_atkin

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

No annotations are provided, so the description must fully disclose behavioral traits. It fails to describe what the tool does (e.g., generates prime numbers), its output format, performance characteristics beyond 'better asymptotic complexity', or any side effects. This leaves critical behavioral information unspecified.

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 brief and to the point, consisting of a single sentence that identifies the algorithm and its complexity, followed by domain/category tags. It is front-loaded with the algorithm name, but could be more informative without sacrificing conciseness.

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?

Given the lack of annotations, no output schema, and minimal parameter documentation, the description is incomplete. It does not explain what the tool returns, how to interpret results, or provide enough context for effective use, especially compared to other prime-related tools in the sibling list.

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?

The input schema has 1 parameter with 0% description coverage, and the description does not explain the 'limit' parameter's meaning (e.g., upper bound for prime generation). Without any parameter details in the description, it does not compensate for the low schema coverage, leaving the parameter undocumented.

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 the tool implements the 'Sieve of Atkin' algorithm, which is a modern sieve with better asymptotic complexity, and provides domain/category context. However, it does not specify the exact verb (e.g., 'generate primes up to a limit') or clearly distinguish it from sibling tools like 'sieve_of_eratosthenes' or 'incremental_sieve', making the purpose somewhat vague.

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 offers no guidance on when to use this tool versus alternatives. It does not mention any specific use cases, prerequisites, or comparisons with other prime-generation tools in the sibling list, leaving the agent with no usage instructions.

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