Burs-IA Utils

Factorización en primos

prime-factorize

Read-onlyIdempotent

Factoriza un entero (hasta 10^20) en primos con exponentes y cuenta de divisores. Cuándo: un resultado numérico tiene que ser exacto o reproducible y no estimado. No para: probar la primalidad con Miller-Rabin determinista hasta 3,3·10^24 y devolver los primos siguiente y anterior (is-prime). Efectos secundarios: ninguno (solo lectura, sin red, sin estado guardado). Determinista: la misma entrada da la misma salida. Límites: entrada JSON de hasta 64 KB, 1 s por llamada, resultado de hasta 1 MB.

EN: Factorizes an integer up to 10^20 into primes (trial division plus Pollard rho), returning factors with exponents and the divisor count. When: a numeric result has to be exact or reproducible instead of estimated. Not for: testing primality with deterministic Miller-Rabin for integers up to 3.3·10^24 (is-prime). Side effects: none (read-only, no network access, no stored state). Deterministic: the same input gives the same output. Limits: JSON input up to 64 KB, 1 s per call, result up to 1 MB.

Input Schema

Name	Required	Description	Default
`n`	Yes	Integer ≥ 2 (integer or string; required; up to 22 chars; pattern ^-?\d{1,21}$).

Output Schema

Name	Required	Description	Default
`n`	No
`factors`	No
`is_prime`	No
`divisor_count`	No

Schema Changelog

Changes observed during successful MCP inspections.

Changed1 schema field changedNov 2, 2026
- addedInput schema / properties / n / examples
```
Added value: +[
+  360
+]
```
First observedNov 1, 2026

TDQS

A4.6/5.0

Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnly/idempotent/non-destructive/closed-world, but the description adds genuine context: no network, no stored state, determinism guarantee, and concrete limits (64 KB input, 1 s per call, 1 MB result). Only slight duplication of the read-only/no-network claim already implied by annotations.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loaded with purpose, then When/Not-for/Side-effects/Deterministic/Limits in a scannable order. The full Spanish and English duplication roughly doubles the length, which is the main cost.

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

Completeness5/5

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

With one parameter and an output schema present, the description needn't explain return shape; it still covers domain bounds, performance limits, determinism, and the sibling split. Nothing needed to invoke it correctly is missing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100% and documents the single parameter (integer or string, pattern, 22 chars), but the description adds the meaningful bound of 10^20 that the schema does not express, clarifying the practical domain.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb and resource — factorizes an integer up to 10^20 into primes with exponents and divisor count — plus the algorithm used (trial division + Pollard rho). An agent can distinguish it from numeric siblings without opening the schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines5/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Explicit 'When' clause (results must be exact/reproducible, not estimated) and an explicit 'Not for' clause naming the alternative is-prime with its own bound (3.3·10^24) and behavior (next/previous prime). Routing is unambiguous.

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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