# Numora Mersenne Number Endpoint

> Numora Mersenne Number Endpoint is a paid API for AI agents from numorapoi.orbonomy.xyz, paid per call via x402, $0.03/call, status unknown (last checked 2026-09-15).

Computes the Mersenne number for a given integer exponent (2^p - 1), returning the full result and a human-readable computation description.

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/number/mersenne
- Price: $0.03/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-computation-4535c158
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_3HtQl3EOKVpOU2ysr8xal

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-computation-4535c158 -d '<json body>'
```

Example prompt: What is the Mersenne number for exponent 31? Use the Numora pure math API to compute 2^31 - 1 exactly.

## When to prefer this

Use this endpoint when you need to compute a Mersenne number (2^p - 1) for a specific integer exponent without any external dependencies. Ideal for number theory tasks, primality research, cryptographic key research, or educational math applications that require exact large-integer results.

## Known failure modes

- Missing required 'exponent' field returns validation error
- Non-integer or negative exponent may return an error or undefined result
- Very large exponents may cause timeout or computation overflow
- Payment failure via x402 returns 402 Payment Required before computation occurs

## 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 a boolean success flag, a result object containing the computed Mersenne number (2^exponent - 1), and a human-readable computation 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-computation-4535c158/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numorapoi.orbonomy.xyz](https://www.zero.xyz/host/numorapoi.orbonomy.xyz/llms.txt)