ScorpTech x402 Tools

Proth

proth

Read-onlyIdempotent

The Proth number k2^n + 1. k must be odd and strictly less than 2^n. 12^1+1 is 3, and 3*2^5+1 is 97. An even k, or a k that is not below 2^n, is rejected. n runs from 1 to 40. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/proth

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": {
      "k": "<k>",
      "n": "<n>"
    },
    "name": "proth"
  }
}

Input Schema

Name	Required	Description	Default
`k`	Yes
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.1/5.0

Behavior4/5

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

Beyond the annotations (readOnly, idempotent, openWorld) the description adds real operational context: a $0.001 USDC x402 payment per successful call on Solana and an equivalent HTTPS endpoint. What it does not disclose — with no output schema — is what a successful call actually returns (the Proth number? a primality verdict?), which is the main remaining blind spot.

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?

Front-loaded with the definition and validation rules, then pricing, then transport — a sensible order and no filler. Minor redundancy in restating the admissibility rule a second time ('An even k, or a k that is not below 2^n, is rejected').

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

Completeness3/5

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

For a tool with no output schema and no annotations covering results, the description should state what is returned; instead it only describes input rejection, leaving the output ambiguous (value of k*2^n+1 vs. a Proth-prime test). Pricing and endpoint coverage are good, but the return-value gap is material for a 2-parameter compute tool.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters5/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 0%, so the description carries the full burden and does it well: k must be odd and strictly below 2^n, n is bounded to 1..40, and two concrete examples anchor the semantics. The only omission is the schema's large upper bound on k, which the k < 2^n rule effectively supersedes.

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 a precise mathematical object with its defining formula (k*2^n + 1), the exact admissibility conditions (k odd, k < 2^n) and worked examples (3, 97). An agent can distinguish this from neighbours like pierpont, cullen, woodall or kynea, which use different forms, without opening any schema.

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?

The description defines the valid input domain ('an even k, or a k that is not below 2^n, is rejected') but never says when to reach for this tool versus the many sibling number tools, nor what distinguishes it as a check versus a generator. Usage is implied by the constraints rather than stated.

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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