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IBM

MCP Math Server

by IBM

segmented_sieve

Find prime numbers within a specified range using a memory-efficient algorithm. This tool calculates all primes between given low and high values with optimized resource usage.

Instructions

Segmented sieve for finding primes in a range [low, high] with memory efficiency. (Domain: arithmetic, Category: sieve_algorithms)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
lowYes
highYes
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 'memory efficiency,' which hints at performance characteristics, but fails to describe critical behaviors: what the tool returns (e.g., a list of primes, a count), any limitations (e.g., range size constraints, computational complexity), error handling, or side effects. 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 extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and key feature ('memory efficiency'). Every word earns its place, with no redundant information or fluff. The domain and category annotations are efficiently appended in parentheses, maintaining clarity without verbosity.

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 (a computational algorithm with 2 parameters), lack of annotations, and no output schema, the description is incomplete. It doesn't explain what the tool returns (e.g., a list of primes, a count, or an error for invalid inputs), performance implications, or usage context. For a tool with no structured data to rely on, this leaves significant gaps in understanding how to effectively use it.

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, so the description must compensate. It adds meaning by specifying that parameters define a range '[low, high]' for finding primes, which clarifies the purpose of 'low' and 'high' beyond their schema types. However, it doesn't detail constraints (e.g., that 'low' and 'high' must be non-negative integers, or that 'low' <= 'high'), leaving some semantics incomplete. This partial compensation justifies a baseline score.

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: 'Segmented sieve for finding primes in a range [low, high] with memory efficiency.' It specifies the verb ('finding primes'), resource ('range [low, high]'), and a key characteristic ('memory efficiency'), distinguishing it from simpler prime-finding tools like 'sieve_of_eratosthenes' or 'incremental_sieve' in the sibling list. However, it doesn't explicitly differentiate from all siblings (e.g., 'prime_counting_sieve'), keeping it from 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 'memory efficiency' but doesn't specify scenarios where this is advantageous (e.g., large ranges) or when other tools like 'sieve_of_eratosthenes' might be preferable. There are no explicit when/when-not statements or named alternatives, leaving usage unclear.

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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