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IBM

MCP Math Server

by IBM

sexy_primes

Find prime number pairs that differ by 6 within a specified limit. This tool identifies sexy prime pairs for mathematical analysis and pattern recognition.

Instructions

Find all sexy prime pairs (primes differing by 6) 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 the tool finds prime pairs but does not describe output format, performance characteristics (e.g., computational limits), error handling, or whether it's read-only or mutative. For a tool with no annotations, this is a significant gap in transparency.

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 highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by domain and category in parentheses. Every element earns its place with no redundant information, making it efficient and easy to parse.

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

Completeness3/5

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

Given the tool's low complexity (one parameter, no output schema, no annotations), the description is minimally adequate. It explains what the tool does but lacks details on behavior, output format, and usage context. While it meets basic requirements, it does not fully compensate for the absence of structured data like annotations or output schema.

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 0% description coverage, with one parameter 'limit' of type integer. The description adds context by specifying 'up to limit', implying an upper bound for the search. However, it does not detail constraints (e.g., minimum value, handling of invalid inputs) or examples, providing only basic semantic clarification beyond the schema.

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 sexy prime pairs (primes differing by 6) up to limit.' It specifies the verb ('Find'), resource ('sexy prime pairs'), and scope ('up to limit'), making it easy to understand what the tool does. However, it does not explicitly differentiate from sibling tools like 'cousin_primes' or 'twin_prime_pairs', which also find prime pairs with specific differences.

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 does not specify scenarios, prerequisites, or comparisons to sibling tools such as 'cousin_primes' or 'twin_prime_pairs'. This leaves the agent without explicit usage instructions.

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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