# Numora Prime Factorization API

> Numora Prime Factorization API is a paid API for AI agents from numorapoi.orbonomy.xyz, paid per call via x402, $0.03/call, status unknown (last checked 2026-09-14).

Computes the complete prime factorization of a given integer, returning its prime factors and their exponents

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/number/prime-factorization
- Price: $0.03/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-207fe67c
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_XHU7BNcFE6ua-oFLxARSP

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-207fe67c -d '<json body>'
```

Example prompt: What is the prime factorization of 1260? Break it down into its prime factors with exponents.

## When to prefer this

Use this endpoint when you need accurate, server-side prime factorization of an integer without implementing the algorithm yourself — especially useful in number theory workflows, cryptographic analysis helpers, educational tools, or math pipelines where you want zero local dependencies and pay-per-use pricing via x402 micropayments on Base.

## Known failure modes

- Non-integer input causes validation error
- Missing required field 'n' returns error
- Very large integers may exceed computation limits
- Payment failure via x402 micropayment returns 402 status
- Negative or zero input may return error or be undefined behavior

## 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=true, a result object containing the prime factors and their exponents for the given integer, and a human-readable computation string describing 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-207fe67c/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)