Math & Numbers
Smallest primitive root mod n with certificate g^(φ/q) ≠ 1, root count φ(φ(n)), up to 50 listed roots, and candidate verification. n ≤ 10¹².
Call this tool from your code in three languages.
curl -X POST 'https://api.elysiatools.com/en/api/tools/primitive-root-finder' \
-H 'Content-Type: application/json' \
-d '{"n":"23","mode":"list","g":""}'Send a POST request with your inputs as JSON. File parameters require a separate upload first.
POST https://api.elysiatools.com/en/api/tools/primitive-root-finder| Name | Type | Required | Description |
|---|---|---|---|
| n | text | Yes | 2 ≤ n ≤ 10¹² (trial-division factorization bound). |
| mode | select | Yes | — |
| g | text | No | Required when verifying; reduced modulo n automatically. |
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-primitive-root-finder": {
"name": "primitive-root-finder",
"description": "Smallest primitive root mod n with certificate g^(φ/q) ≠ 1, root count φ(φ(n)), up to 50 listed roots, and candidate verification. n ≤ 10¹².",
"baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=primitive-root-finder",
"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": "primitive-root-finder",
"arguments": {
"n": "23",
"mode": "list",
"g": ""
}
}
}Questions or issues? Contact [email protected]