ScorpTech x402 API

Primorial

primorial

Read-onlyIdempotent

The primorial of n, the product of the primes less than or equal to n. The primorial of 1 is 1, of 10 is 210, and of 11 is 2310. n runs from 1 to 5000. 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/primorial

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": "primorial"
  }
}

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 safety, and the description adds genuinely new operational context: a per-call price ($0.001 USDC via x402 on Solana), an equivalent HTTPS endpoint, and the output-type switch to a decimal string past 15 digits. Only error/failure 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.

Conciseness5/5

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

Definition first, then examples, domain, output-format caveat, then pricing/endpoint — all front-loaded and every sentence carries information. No filler or restatement of the title.

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?

With no output schema, the description usefully explains that large results arrive as decimal strings, and it covers cost and transport. It is close to complete for a one-parameter compute tool, missing only error semantics and sibling disambiguation.

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% (the property has no description, only min/max bounds), so the description must compensate; it does by defining what n means mathematically, restating the 1–5000 domain in prose, and illustrating boundary behavior with examples. It does not say what happens for invalid or out-of-range n.

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?

It gives a precise mathematical definition (product of primes ≤ n) plus concrete examples (1→1, 10→210, 11→2310), so an agent knows exactly what is computed. It does not differentiate itself from the sibling primorial_prime, which is the only remaining 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?

There is no explicit when-to-use/when-not-to guidance or named alternative, though a pure math function with a single numeric input has implied usage. The examples implicitly clarify semantics but do not route the agent between primorial and primorial_prime.

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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