Primes

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

numbers.prime · v1 · renderer text

11534840843916203537
10984643855200244651
15815691545331699991
15814055605688551481
9517388736829049113

Controls · from schema()

Bit width

8 256

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.

How many

1 20

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.

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.

Show as

Entropy source

Picking a source changes the story on the receipt, never the quality: anything below class A is mixed with the OS CSPRNG before it reaches you. This result actually came from RANDOM.ORG.

There is no same-seed re-render here. Recomputing a secret from a kept seed is exactly the thing this generator refuses to make possible, so every change of parameters draws fresh entropy.

seed token withheld

Nothing to keep: no token is issued for a generator that makes secrets.

entropy in

16 bytes

stream used

4,792 bytes

rejections

duration

23,611 µs

bits

found

candidates tested

157

rejected by trial division

131

expected candidates per prime

22.20

rounds

false positive bound

4^-40, about 1 in 10^24 — far below the odds of the hardware getting the arithmetic wrong

exhausted

search budget

643

sensitive

yes

Seed receipt

Class A · Cryptographic

Atmospheric radio noise, sampled in Dublin moments ago.

source: RANDOM.ORG
observed: 2026-10-30T11:15:38+00:00
latency: 291ms
mixed with: csprng — always

https://www.random.org/randomness/ ↗

No permalink

This generator makes secrets, so it is never given a shareable link. A password with a replayable URL is not a password — anyone holding the link could recompute it byte for byte, forever. The seed token is discarded the moment the response is written; nothing here is stored, logged or recoverable.

seed · withheld by design · numbers.prime is marked sensitive

This page and /api/v1/g/numbers.prime run the same code. There is no private endpoint.

Primes

Result

Measurements

Seed receipt

No permalink