ScorpTech x402 API

Fermat Number

fermat_number

Read-onlyIdempotent

The Fermat number 2^(2^n) + 1. n=0 gives 3, n=4 gives 65537, and n=5 gives 4294967297. n runs from 0 to 12. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/fermat-number

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": {
      "n": "<n>"
    },
    "name": "fermat_number"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.9/5.0

Behavior4/5

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

Annotations already cover read-only, idempotent, non-destructive and open-world, so the safety profile is settled. Beyond that, the description adds genuinely useful behavior: values past 15 digits are returned as a decimal string, calls cost $0.001 USDC via x402 on Solana, and an equivalent HTTPS endpoint is provided. Only the failure/out-of-range behavior is left unstated.

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?

The definition is front-loaded with the formula and sample outputs, then trails into practical details (string output threshold, price, URL). Compact with no filler, though the pricing/endpoint clauses are somewhat orthogonal to the mathematical purpose.

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 single-parameter, no-output-schema computation tool, everything needed to call it correctly is present: the formula, the valid range, example outputs, the switch to string representation, and the cost of invocation. Nothing material 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 description coverage is 0%, so the description must carry the meaning of n. It does so via the defining formula and three concrete n-to-value examples, which is more than the bare integer/min/max bounds in the schema. The range restatement is redundant with the schema, but the semantic anchoring is not.

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 gives an explicit verb-equivalent (computes) and resource (the Fermat number), backed by the closed-form 2^(2^n)+1 and concrete worked values for n=0, 4, 5. It is unmistakable what the tool returns, though it never names or distinguishes the sibling fermat_prime, which an agent could plausibly confuse with this.

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 only implied: the stated n range (0-12) and example values make the intended call pattern obvious. There is no explicit when-to-use or when-not guidance, and no pointer to the adjacent fermat_prime tool for primality-related questions.

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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