# Primes — Randomly

> Miller–Rabin, forty rounds, at the bit width you ask for. One of 63 generators at [Randomly](https://randomly.cluxnei.dev), a library of random generators seeded from verifiable real-world entropy. Free HTTP API, no key, no signup.

## `numbers.prime` — Primes

Miller–Rabin, forty rounds, at the bit width you ask for.

| | |
|---|---|
| **Key** | `numbers.prime` |
| **Module** | `numbers` |
| **Version** | `1` — a permalink carries this, and a replay against a different version returns `409` rather than something else |
| **Formats** | `application/json`, `text/plain` |
| **Studio** | https://randomly.cluxnei.dev/g/numbers/prime |
| **API** | `GET https://randomly.cluxnei.dev/api/v1/g/numbers.prime` |

`value` is the result itself — one value, or a list of them; `display` is the same thing rendered as a single human-readable string.

**Sensitive.** This generator produces secrets, so it is given no token and no shareable
permalink, and `/api/v1/replay` returns `404` for it. A secret with a replayable URL is
not a secret. Nothing is logged or stored either way — there is no database.

| Parameter | Type | Default | Accepts | What it does |
|---|---|---|---|---|
| `bits` | int | `64` | `8` – `256` | Bit width — A 2048-bit RSA key is two 1024-bit primes. This stops at 256 because bcmath does the modular exponentiation in software and the wait stops being interactive. |
| `count` | int | `5` | `1` – `20` | How many |
| `safe` | bool | `false` | `true`, `false` | Safe primes only — p where (p−1)/2 is also prime — what Diffie–Hellman wants. Rarer by another factor of ln(p), so the width is capped at 128 bits when this is on. |
| `twin` | bool | `false` | `true`, `false` | Prefer twins — Report whether p + 2 is also prime. Not a filter: twin primes thin out fast and searching for them at 64 bits would hang. |
| `format` | enum | `decimal` | `decimal`, `hex`, `both` | Show as |

Out-of-range numbers are **clamped, not rejected**, so a request never fails for being
ambitious — but it may not do what you meant. Unknown keys are dropped and missing ones
fall back to the defaults above.

```bash
curl -s 'https://randomly.cluxnei.dev/api/v1/g/numbers.prime?bits=64&count=5&safe=0' -H 'Accept: text/plain'
```

## The receipt

Every result carries one, naming the physical source of the randomness and linking to the
third party's own record of it:

```json
"receipt": {
  "source": "seismic",
  "source_label": "USGS Seismic Feed",
  "class": "C",
  "caveat": "Carries only tens of bits of genuine surprise. Always mixed with the OS CSPRNG.",
  "narrative": "A magnitude 3.6 earthquake, 67 km N of Culebra, Puerto Rico, 39.6 km down — 52 minutes ago.",
  "proof_url": "https://earthquake.usgs.gov/earthquakes/eventpage/us7000th33",
  "mixed_with_csprng": true,
  "degraded": false
}
```

Pick the source with `?source=`, or leave it at the default `auto`:

- **Class A** (Cryptographic) — `csprng`, `anu-qrng`, `random-org`
- **Class B** (Public beacon) — `nist-beacon`, `drand`, `bitcoin`. Published openly — anyone can look this value up after the fact.
- **Class C** (Observational) — `seismic`, `space-weather`, `atmosphere`, `iss`. Carries only tens of bits of genuine surprise. Always mixed with the OS CSPRNG.

## More

- [The full API contract](https://randomly.cluxnei.dev/api.md)
- [Everything in one file](https://randomly.cluxnei.dev/llms-full.txt)
- [The catalogue as JSON](https://randomly.cluxnei.dev/api/v1/generators)
- [This generator in the browser](https://randomly.cluxnei.dev/g/numbers/prime)