Math & Numbers
(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.
Call this tool from your code in three languages.
curl -X POST 'http://127.0.0.1:3003/en/api/tools/wilson-theorem-checker' \
-H 'Content-Type: application/json' \
-d '{"n":"13","detail":"trace"}'Send a POST request with your inputs as JSON. File parameters require a separate upload first.
POST http://127.0.0.1:3003/en/api/tools/wilson-theorem-checker| Name | Type | Required | Description |
|---|---|---|---|
| n | text | Yes | 2 ≤ n ≤ 10⁷ (one factorial-modulo pass). |
| detail | select | Yes | — |
Text result
{
"result": "Processed text content",
"error": "Error message (optional)",
"message": "Notification message (optional)",
"metadata": {
"key": "value"
}
}Add this tool to your Model Context Protocol server so AI agents can list and call it.
Add this block to your MCP client configuration:
{
"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": "http://127.0.0.1:3003/mcp/sse?toolId=wilson-theorem-checker",
"command": "",
"args": [],
"env": {},
"isActive": true,
"type": "sse"
}
}
}After connecting to the SSE endpoint, list the exposed tools:
{
"jsonrpc": "2.0",
"id": 1,
"method": "tools/list"
}Invoke the tool by its id, passing arguments built from its parameters:
{
"jsonrpc": "2.0",
"id": 2,
"method": "tools/call",
"params": {
"name": "wilson-theorem-checker",
"arguments": {
"n": "13",
"detail": "trace"
}
}
}Questions or issues? Contact [email protected]