ScorpTech x402 Tools

Wilson Quotient

wilson_quotient

Read-onlyIdempotent

The Wilson quotient ((p-1)! + 1) / p for a prime p. The quotient of 5 is 5, of 7 is 103, and of 13 is 36846277. A composite is rejected. p runs from 2 to 100. This checks the given prime. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/wilson-quotient

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>"
    },
    "name": "wilson_quotient"
  }
}

Input Schema

Name	Required	Description	Default
`p`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.2/5.0

Behavior4/5

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

Annotations already declare readOnly/idempotent/non-destructive, but the description adds genuinely new behavior: invalid-input rejection for composites, the valid domain 2..100, and pricing/payment requirements ($0.001 USDC per successful call via x402 on Solana) with an alternative HTTPS endpoint. What it does not cover is error/response shape beyond 'rejected'.

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?

Front-loaded with the defining formula, then examples, then the domain constraint, then cost/transport. Worked examples earn their place by showing the output type, and nothing is padded.

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

Completeness4/5

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

There is no output schema, but the worked examples effectively communicate the return value (a large integer). Combined with the domain restriction and pricing note, an agent has enough to call it correctly; only explicit failure/response behavior is left thin.

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 0%, so the description must carry the load, and it does: it declares p must be a prime and that p runs from 2 to 100, adding the primality constraint that the bare integer schema (minimum 2, maximum 100) does not express.

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 the exact mathematical object with its formula, '((p-1)! + 1) / p for a prime p', plus concrete output examples (5, 103, 36846277). An agent can immediately tell this computes a Wilson quotient rather than testing primality (wilson_prime) or a related number-theoretic function.

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?

Constrains usage usefully: p must be prime (composites rejected) and must lie in 2..100. However, no sibling is named or contrasted — notably wilson_prime in the same family — so the agent must infer when this is preferable to neighbor tools.

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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