Math & Numbers

Wilson's Theorem Primality Checker

(n−1)! ≡ −1 (mod n) ⟺ n is prime. Exact factorial residue for n ≤ 10⁷, Miller–Rabin cross-check, composite factorial law, optional running-products trace.

text· Text resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/wilson-theorem-checker' \
  -H 'Content-Type: application/json' \
  -d '{"n":"13","detail":"trace"}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST https://api.elysiatools.com/en/api/tools/wilson-theorem-checker

Parameters

Name	Type	Required	Description
n	text	Yes	2 ≤ n ≤ 10⁷ (one factorial-modulo pass).
detail	select	Yes	—

Response format

Text result

JSON

{
  "result": "Processed text content",
  "error": "Error message (optional)",
  "message": "Notification message (optional)",
  "metadata": {
    "key": "value"
  }
}

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-wilson-theorem-checker": {
      "name": "wilson-theorem-checker",
      "description": "(n−1)! ≡ −1 (mod n) ⟺ n is prime. Exact factorial residue for n ≤ 10⁷, Miller–Rabin cross-check, composite factorial law, optional running-products trace.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=wilson-theorem-checker",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "wilson-theorem-checker",
    "arguments": {
  "n": "13",
  "detail": "trace"
}
  }
}

Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

Questions or issues? Contact [email protected]

Browse tools Open tool

Name

Type

Required

Description

text

Yes

2 ≤ n ≤ 10⁷ (one factorial-modulo pass).

detail

select

Yes

—

{ "mcpServers": { "elysiatools-wilson-theorem-checker": { "name": "wilson-theorem-checker", "description": "(n−1)! ≡ −1 (mod n) ⟺ n is prime. Exact factorial residue for n ≤ 10⁷, Miller–Rabin cross-check, composite factorial law, optional running-products trace.", "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=wilson-theorem-checker", "command": "", "args": [], "env": {}, "isActive": true, "type": "sse" } } }