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IBM

MCP Math Server

by IBM

prime_gap_records

Find first occurrences of prime gaps to explore distribution patterns in prime numbers. Input a limit to retrieve record gaps up to that value.

Instructions

Find record prime gaps (first occurrence of each gap size). (Domain: arithmetic, Category: prime_conjectures)

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 mentions the action ('Find') but does not describe what the tool returns (e.g., a list of gaps, their sizes, or associated primes), any computational limits, or error conditions. 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 and front-loaded, consisting of a single, direct sentence that states the tool's purpose. There is no wasted language, and the parenthetical domain/category note adds context without verbosity. It efficiently communicates the core function.

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 (involving prime gaps), lack of annotations, no output schema, and undocumented parameters, the description is insufficient. It does not explain the return format, computational behavior, or parameter meaning, leaving the agent with inadequate information to use the tool effectively.

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 one parameter ('limit') with 0% description coverage, meaning its purpose is undocumented. The description does not explain what 'limit' represents (e.g., upper bound for prime search, maximum gap size to consider, or number of gaps to return). This lack of semantic information hampers effective tool invocation.

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 record prime gaps (first occurrence of each gap size).' It specifies the verb ('Find'), resource ('record prime gaps'), and scope ('first occurrence of each gap size'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'prime_gap' or 'prime_gaps_analysis', which is why it doesn't achieve 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 lacks any mention of prerequisites, context, or comparisons with sibling tools such as 'prime_gap' or 'prime_gaps_analysis'. This absence of usage instructions leaves the agent without clear direction on tool selection.

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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