# Numora Mersenne Number Generator

> Numora Mersenne Number Generator is a paid API for AI agents from numomo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-15).

Computes whether a given integer exponent produces a Mersenne prime (2^p - 1) and returns the resulting Mersenne number and its properties

## Facts

- Endpoint: POST https://numomo.vercel.app/api/number/mersenne
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-mersenne-number-generator-69b87a05
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_ZXgcB_EMV_o5kNsRersL6

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-mersenne-number-generator-69b87a05 -d '<json body>'
```

Example prompt: Can you compute the Mersenne number for exponent 31 and tell me whether it's a Mersenne prime?

## When to prefer this

Choose this endpoint when you need to compute or verify Mersenne numbers (2^p - 1) and their primality for a specific integer exponent, especially in number theory research, educational math contexts, or cryptography applications. Prefer this over general-purpose math libraries when you need a simple pay-per-call API with no setup, and over symbolic math APIs when you want a fast numeric result with a human-readable explanation included.

## Known failure modes

- Missing or non-integer exponent returns a validation error
- Exponent too large may cause timeout or overflow
- Negative or zero exponent may return an error or unexpected result
- Payment failure via x402 returns 402 status before computation begins

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with success (boolean), result (object containing the Mersenne number 2^p-1, whether it is prime, the exponent used, and related numeric properties), and computation (a human-readable string describing what was calculated).

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "exponent"
 ],
 "properties": {
  "exponent": {
   "type": "integer"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-mersenne-number-generator-69b87a05/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numomo.vercel.app](https://www.zero.xyz/host/numomo.vercel.app/llms.txt)