mersenne_numbers

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but lacks critical behavioral details: it doesn't specify the output format (e.g., list of numbers, JSON structure), performance characteristics (e.g., computational limits for large exponents), error handling (e.g., for invalid limits), or whether the limit is inclusive/exclusive. For a tool with no annotations, this leaves significant gaps.

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 concise and front-loaded, with a single sentence that directly states the tool's purpose. The parenthetical domain and category add minor context without unnecessary elaboration. There's no wasted verbiage, making it efficient for quick understanding.

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 complexity (mathematical computation with prime exponents), lack of annotations, and no output schema, the description is incomplete. It doesn't explain what the tool returns (e.g., a list of Mersenne numbers, their values, or just exponents), how results are formatted, or any limitations (e.g., performance with large limits). For a tool with no structured support, more descriptive detail is needed to guide effective use.

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 description mentions the 'limit' parameter implicitly ('for prime exponents up to limit'), but the input schema has 0% description coverage. The description adds some semantic context by clarifying that 'limit' refers to the maximum prime exponent considered, which is useful beyond the bare schema. However, it doesn't detail constraints (e.g., must be positive integer, typical ranges) or examples, leaving room for improvement given the low schema coverage.

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 purpose: 'Generate Mersenne numbers 2^p - 1 for prime exponents up to limit.' It specifies the mathematical operation (generating Mersenne numbers), the formula (2^p - 1), and the constraint (prime exponents up to a limit). However, it doesn't explicitly differentiate from sibling tools like 'mersenne_prime_exponents' or 'is_mersenne_prime', which are related but distinct operations.

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 minimal guidance on when to use this tool. It mentions the domain (arithmetic) and category (special_primes), but offers no explicit advice on when to choose this over alternatives like 'mersenne_prime_exponents' or 'is_mersenne_prime'. There's no mention of prerequisites, typical use cases, or scenarios where this tool is preferred.

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