ScorpTech x402 API

Von Staudt

von_staudt

Read-onlyIdempotent

The von Staudt-Clausen integer. For even m at least 2, B(m) plus the sum of 1/p over primes p with p-1 dividing m is an integer. For m = 2, 4, 6, and 10 that integer is 1. An odd m is rejected. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/von-staudt

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": {
      "m": "<m>"
    },
    "name": "von_staudt"
  }
}

Input Schema

Name	Required	Description	Default
`m`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4/5.0

Behavior4/5

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

Annotations already declare readOnly, idempotent, non-destructive, and openWorld behavior. The description adds useful non-annotation context: odd inputs are rejected, pricing is $0.001 USDC per successful call, payment is via x402 on Solana, and an HTTPS endpoint is provided.

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 compact and front-loaded: it names the object, states the formula, gives examples, states the rejection rule, and then records payment and endpoint details. Every sentence adds useful information.

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?

For a one-parameter calculator with no output schema, the description sufficiently defines the mathematical output as an integer and provides examples. It still leaves the m=0 edge case and exact response format unstated, but annotations cover the safety profile.

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?

Schema description coverage is 0%, so the description must carry parameter meaning. It gives valid parity and examples for m, but does not clarify m=0 despite the schema minimum being 0, does not mention the maximum of 40, and leaves B(m) undefined.

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 identifies a specific mathematical object, the von Staudt-Clausen integer, and explains the formula and output examples. It is clear what the tool computes, but it does not explicitly distinguish itself from related sibling tools such as bernoulli or bernoulli_denom.

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

Usage Guidelines4/5

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

It clearly states that even m at least 2 is the intended domain and that odd m is rejected, giving concrete examples for m=2,4,6,10. It does not compare this tool with alternatives for related Bernoulli-number computations.

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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