ScorpTech x402 Tools

Mersenne Prime

mersenne_prime

Read-onlyIdempotent

Whether 2^n - 1 is prime. Exponents 2, 3, 5, 7, 13, 17, 19, and 31 are, inside this cap. Exponent 11 is not, because 2047 = 23*89. n runs from 2 to 31. This checks the given exponent. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/mersenne-prime

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": "mersenne_prime"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.7/5.0

Behavior4/5

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

Annotations already cover read-only/idempotent/non-destructive, and the description adds genuinely new behavioral context: cost of $0.001 USDC per successful call via x402 on Solana and an equivalent HTTPS endpoint, which matters for payment/auth planning. It also pre-discloses the answer for every valid input (the prime exponents), which is unusually transparent for a deterministic predicate.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness3/5

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

The core predicate is front-loaded and the cost/endpoint info is useful, but the enumerations ("2, 3, 5, 7, 13, 17, 19, and 31") and the worked counterexample "2047 = 23*89" consume space without helping an agent decide or invoke. Tightening to purpose + range + cost would lose nothing.

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 deterministic math predicate with full annotation coverage and no output schema, the description supplies everything needed: what is computed, the valid input range, the cost model, and a fallback transport. Only the relationship to the sibling `mersenne` tool is left unstated.

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% and the schema only constrains `n` to an integer 2..31; the description supplies the missing meaning by identifying n as the exponent in 2^n - 1 and restating the inclusive range. It does not add format or edge-case detail beyond that, but the semantics are now unambiguous.

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 phrase "Whether 2^n - 1 is prime" gives a precise predicate over a named mathematical object, and "This checks the given exponent" confirms it is a single-value test rather than an enumeration. It does not, however, distinguish itself from the sibling `mersenne` (likely the number generator) or `prime_check`, so an agent must infer the split.

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 implied by the domain constraint ("n runs from 2 to 31", "checks the given exponent"), which tells an agent the input envelope. But there is no explicit when-to-use/when-not statement and no named alternative for computing 2^n - 1 itself versus testing its primality.

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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