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IBM

MCP Math Server

by IBM

prime_quadruplets

Find all prime quadruplets up to a specified limit to identify clusters of four consecutive prime numbers with specific spacing patterns.

Instructions

Find all prime quadruplets up to limit. (Domain: arithmetic, Category: prime_patterns)

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 what the tool does but lacks details on behavioral traits such as performance characteristics (e.g., computational complexity for large limits), error handling, or output format. For a tool with no annotations, this is a significant gap, as the agent cannot infer these critical aspects from the description alone.

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: 'Find all prime quadruplets up to limit.' The additional context ('Domain: arithmetic, Category: prime_patterns') is brief and relevant. There is no wasted verbiage, and every sentence earns its place by providing essential information efficiently.

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 number calculations and the lack of annotations and output schema, the description is incomplete. It does not explain what a prime quadruplet is, the expected output format, or any limitations (e.g., performance for large limits). For a tool with no structured metadata, the description should provide more context 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 input schema has 1 parameter with 0% description coverage, so the schema provides no semantic information. The description mentions 'limit' but does not explain its meaning, constraints (e.g., must be positive integer), or units. It adds minimal value beyond the schema, but since there is only one parameter, the baseline is higher than for tools with many undocumented parameters.

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 prime quadruplets up to limit.' It specifies the verb ('Find'), resource ('prime quadruplets'), and scope ('up to limit'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'prime_triplets' or 'cousin_primes', which is why it doesn't reach a score of 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_patterns'), but this is too vague to help an agent choose between similar tools like 'prime_triplets' or 'cousin_primes'. There are no explicit instructions on when or when not to use it, or what alternatives exist.

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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