# Numora Prime Factorization API

> Numora Prime Factorization API 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 the complete prime factorization of a given integer, returning all prime factors and their exponents.

## Facts

- Endpoint: POST https://numomo.vercel.app/api/number/prime-factorization
- 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-prime-factorization-api-407a72eb
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_KvLTfYcMa_2fqw_s4_V1A

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-407a72eb -d '<json body>'
```

Example prompt: What is the prime factorization of 360? Break it down into all its prime factors with their exponents.

## When to prefer this

Choose this endpoint when you need a deterministic, server-side prime factorization of an integer without writing or executing local code. It is ideal for AI agents that need verified number-theoretic computations on demand, especially in math tutoring, cryptography analysis, or educational contexts. Prefer it over general-purpose code execution when you want a clean, structured JSON response with no setup overhead.

## Known failure modes

- Missing required field 'n' returns a validation error
- Non-integer or float input may be rejected or produce unexpected results
- Very large integers may time out or return errors depending on server limits
- Negative integers or zero may be unsupported edge cases
- Insufficient x402 micropayment balance causes a payment-required error

## 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 'computation' string describing what was computed, and a 'result' object containing the prime factors of the input integer along with their respective exponents or multiplicities.

## 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-407a72eb/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)