ScorpTech x402 Tools

Factorial Valuation

factorial_valuation

Read-onlyIdempotent

The p-adic valuation of n!, the exponent of the prime p in n!. v_2(10!) is 8, v_3(10!) is 4, and v_2(100!) is 97. p must be prime. n runs from 0 to 1000000000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/factorial-valuation

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "p": "<p>",
      "n": "<n>"
    },
    "name": "factorial_valuation"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes
`p`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.3/5.0

Behavior4/5

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

The description adds substantial context beyond the annotations: it discloses the $0.001 USDC per-successful-call pricing via x402 on Solana, provides an HTTPS endpoint, and states the prime and range constraints. It stops short of explaining error behavior for invalid p or the exact return type, but the examples implicitly show an integer result.

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 definition is front-loaded and compact. Every sentence supplies useful information: mathematical meaning, worked examples, prime constraint, n range, pricing, and an alternate HTTPS endpoint.

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?

For a two-parameter mathematical function with no output schema, the description is complete enough to invoke correctly: it defines the operation, constrains p and n, gives examples of expected outputs, and discloses payment and endpoint details.

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 description coverage is 0%, so the description must carry parameter meaning; it does so by defining p as a prime and n as ranging from 0 to 1000000000000. It does not restate p's upper bound or explicitly say n is an integer, but the schema covers numeric bounds and the examples clarify the intended semantics.

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?

The description states a precise mathematical operation: the p-adic valuation of n!, defined as the exponent of prime p in n!. It is specific enough to distinguish this from general p-adic or factorial tools, and examples like v_2(10!) = 8 remove ambiguity.

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

Usage Guidelines3/5

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

Usage is implied by the exact mathematical definition, and constraints such as 'p must be prime' help guide correct invocation. However, it does not explicitly say when to use this versus related siblings such as padic, factorial_mod, or kummer, nor does it name any alternative.

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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