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IBM

MCP Math Server

by IBM

prime_constellations

Find prime constellations by specifying a pattern and limit to identify clusters of prime numbers with defined spacing in arithmetic sequences.

Instructions

Find prime constellations of specified pattern. (Domain: arithmetic, Category: prime_patterns)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
patternYes
limitYes
Behavior1/5

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

No annotations are provided, so the description carries full burden for behavioral disclosure. The description only states what the tool does ('Find prime constellations') without explaining how it behaves: no information about output format, performance characteristics, error conditions, or whether it's computationally intensive. This is inadequate for a tool with parameters.

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

Conciseness4/5

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

The description is appropriately concise with two sentences. The first sentence states the core purpose, and the second provides domain/category context. There's no wasted verbiage, though the structure could be improved by front-loading more specific guidance about parameter usage.

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 has 2 required parameters with 0% schema description coverage, no annotations, and no output schema, the description is insufficient. It doesn't explain what prime constellations are, how patterns should be specified, what the output looks like, or any limitations. For a mathematical tool with potentially complex input semantics, this leaves too many gaps.

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

Parameters2/5

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

Schema description coverage is 0%, so the description must compensate for undocumented parameters. The description mentions 'specified pattern' which hints at the 'pattern' parameter, but doesn't explain what format the pattern should take (e.g., array of offsets like [0,2,6] for prime triplets) or what 'limit' means (e.g., maximum number of constellations to find). It adds minimal value beyond the bare parameter names.

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 prime constellations of specified pattern.' It includes a specific verb ('Find'), resource ('prime constellations'), and domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'prime_triplets' or 'prime_quadruplets' that might handle specific constellation patterns, which prevents a perfect score.

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 ('arithmetic') and category ('prime_patterns'), but doesn't specify what constitutes a 'prime constellation' pattern, when this tool is appropriate compared to other prime-related tools, or any prerequisites for usage.

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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