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IBM

MCP Math Server

by IBM

keith_numbers

Calculate Keith numbers up to a specified limit to identify special integer sequences in arithmetic mathematics.

Instructions

Find all Keith numbers up to limit. (Domain: arithmetic, Category: special_numbers)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
limitYes
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 finds numbers 'up to limit,' implying it returns a list or sequence, but does not describe the output format, performance characteristics, error handling, or any side effects. For a tool with no annotations, 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—a single sentence that directly states the tool's purpose and parameter. There is no wasted verbiage; every word contributes essential information. It is front-loaded with the core functionality, making it efficient for quick comprehension.

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

Completeness2/5

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

Given the tool's complexity (mathematical computation with one parameter), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It does not explain what Keith numbers are, the return format, potential performance issues, or error conditions. 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.

Parameters3/5

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

The description mentions the parameter 'limit' and its role ('up to limit'), but the input schema has 0% description coverage, providing only the type (integer). The description adds basic semantic context (it's an upper bound), but does not specify constraints like minimum value, whether it's inclusive/exclusive, or typical ranges. This partially compensates for the low schema coverage but remains minimal.

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: 'Find all Keith numbers up to limit.' It specifies the verb ('Find'), resource ('Keith numbers'), and scope ('up to limit'), which is a well-defined mathematical operation. However, it does not explicitly differentiate from sibling tools like 'is_keith_number' or 'keith_numbers' (if present elsewhere), though the domain/category tags help.

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 mentions the domain and category, but does not indicate prerequisites, typical use cases, or comparisons with related tools (e.g., 'is_keith_number' for checking a single number). The agent must infer usage from context 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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