# Numora Prime Factorization API

> Numora Prime Factorization API is a paid API for AI agents from numormo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-14).

Computes the prime factorization of an integer, returning its prime factors and their exponents.

## Facts

- Endpoint: POST https://numormo.vercel.app/api/number/prime-factorization
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-prime-factorization-api-39095d96
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_e72aie6blFSYX1n-pqsRh

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-prime-factorization-api-39095d96 -d '<json body>'
```

Example prompt: Can you find the prime factorization of 360 for me?

## When to prefer this

Choose this endpoint when you need a reliable, serverless, zero-dependency computation of prime factorization for any integer — especially in agent workflows requiring number theory operations without relying on a general-purpose code executor. Ideal for math tutoring agents, cryptography analysis, divisor counting, and any scenario where you need a structured, machine-readable factorization result rather than a natural language explanation.

## Known failure modes

- Missing required field `n` returns a validation error
- Non-integer or float input may cause a 400 error
- Very large integers may exceed computation limits or time out
- Payment failure or insufficient USDC balance blocks the request via x402
- Negative integers or zero may return an error or undefined behavior depending on implementation

## 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 `success` boolean, a `result` object containing the prime factors and their exponents (e.g. {2: 3, 3: 2, 5: 1} for 360), and a `computation` string with a human-readable description of what was computed.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "n"
 ],
 "properties": {
  "n": {
   "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-prime-factorization-api-39095d96/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numormo.vercel.app](https://www.zero.xyz/host/numormo.vercel.app/llms.txt)