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IBM

MCP Math Server

by IBM

known_fermat_primes

Retrieve the five known Fermat primes for mathematical research and verification of special prime number properties.

Instructions

Get the five known Fermat primes. (Domain: arithmetic, Category: special_primes)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Behavior2/5

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 the tool retrieves the five known Fermat primes, implying a read-only operation that returns a fixed set of data. However, it does not disclose any behavioral traits such as whether the output is static, if there are any rate limits, error conditions, or the format of the return value. For a tool with zero annotation coverage, this leaves significant gaps in understanding its behavior.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is extremely concise and front-loaded: 'Get the five known Fermat primes. (Domain: arithmetic, Category: special_primes)'. Every sentence earns its place by stating the core purpose and providing contextual metadata without unnecessary elaboration. It is appropriately sized for a simple, parameter-less tool.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's simplicity (0 parameters, no annotations, no output schema), the description is minimally adequate. It explains what the tool does but lacks details on output format, behavioral constraints, or usage context. While the absence of an output schema means the description should ideally clarify return values, the tool's straightforward nature (returning a known set of primes) makes the description passable but not fully complete for an agent needing precise execution guidance.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has no parameters (parameter count: 0), and schema description coverage is 100%, meaning the schema fully documents the lack of inputs. The description does not add any parameter information, which is appropriate since no parameters exist. In such cases, a baseline score of 4 is warranted as the description need not compensate for missing parameter details.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose: 'Get the five known Fermat primes.' It specifies the verb ('Get') and resource ('five known Fermat primes'), making the action and target explicit. However, it does not distinguish this tool from potential siblings like 'fermat_numbers' or 'is_fermat_prime', which are listed among the sibling tools, so it lacks sibling differentiation.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides no guidance on when to use this tool versus alternatives. It includes a domain and category ('Domain: arithmetic, Category: special_primes'), but this does not specify usage context, exclusions, or comparisons to sibling tools like 'fermat_numbers' or 'fermat_primality_check'. Without explicit when-to-use instructions, the agent must infer usage from the name and description alone.

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

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