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IBM

MCP Math Server

by IBM

prime_gaps_analysis

Analyze prime number gaps within a specified range to study distribution patterns and identify intervals between consecutive primes.

Instructions

Analyze prime gaps in a given range. (Domain: arithmetic, Category: prime_distribution)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
startYes
endYes
Behavior1/5

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. The description only states what the tool does ('analyze prime gaps') without explaining what 'analyze' entails—such as whether it returns statistical summaries, lists gaps, or performs computations. It fails to disclose critical behavioral traits like output format, computational complexity, or any constraints, leaving the agent with insufficient information to predict the tool's 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, consisting of a single sentence that directly states the tool's purpose, followed by domain and category annotations. There is no wasted verbiage, and the information is front-loaded, making it easy to parse. This efficiency earns a top score for conciseness.

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 complexity of prime gap analysis, the absence of annotations, no output schema, and low parameter schema coverage, the description is incomplete. It does not explain what the analysis entails, what results to expect, or any prerequisites or limitations. For a tool with two parameters and no structured output information, the description fails to provide sufficient context for effective use.

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?

The input schema has 0% description coverage, with two required integer parameters ('start' and 'end') undocumented in the schema. The description mentions 'a given range' but does not elaborate on parameter meanings, valid ranges, or units. This adds minimal semantic value beyond the schema, failing to compensate for the coverage gap, especially since the schema itself lacks descriptions.

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: 'Analyze prime gaps in a given range.' It specifies the verb ('analyze'), resource ('prime gaps'), and scope ('in a given range'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'prime_gap' or 'largest_prime_gap_in_range', which is why it scores a 4 instead of a 5.

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_distribution'), but offers no explicit instructions on when to choose this tool over siblings like 'prime_gap' or 'prime_gap_records'. This lack of comparative context limits its utility for an AI agent.

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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