Is the generated prime truly random?

The candidate is seeded from the Web Crypto API (crypto.getRandomValues), which is a cryptographically secure random source. The number is then tested for primality using Miller-Rabin.

What is the Miller-Rabin test?

Miller-Rabin is a probabilistic primality test. Each round uses a random witness to check whether the number is composite. With 20 rounds, the probability of a composite passing is at most 4^-20 (roughly 1 in 10^12).

Can I use these primes in production cryptography?

This tool is suitable for learning and prototyping. For production RSA or DH keys, use a well-audited library (OpenSSL, libsodium) that also checks safe-prime conditions and other hardening requirements.

Why does generation sometimes take several seconds?

The tool generates random odd candidates and tests each one. At 2048 bits the search can require dozens of candidates before finding a prime. This is normal — prime density near N is roughly 1/ln(N).

What does "bit length" mean for a prime?

A 1024-bit prime is a number between 2^1023 and 2^1024 - 1. The top bit is always set so the prime has exactly the requested bit length.

How many Miller-Rabin rounds should I use?

The default 20 rounds gives an error probability below 10^-12, which is more than sufficient for cryptographic use. Reduce rounds only if you need faster generation at smaller bit lengths.

Cryptographic Prime Number Generator

Name: Cryptographic Prime Number Generator
Availability: InStock
Author: Nham Vu

Generate large random prime numbers (8–2048 bits) using the Miller-Rabin probabilistic primality test — entirely in your browser.

Generator Settings

Bit Length 512

bits (8 – 2048)

Miller-Rabin Rounds

Choose a bit length and click Generate Prime

Copied!

Summary

Generate large random prime numbers (8–2048 bits) using the Miller-Rabin probabilistic primality test — entirely in your browser.

How it works

Choose a bit length between 8 and 2048 using the slider or input field.
Select the number of Miller-Rabin rounds (more rounds = higher certainty, slower).
Click "Generate Prime" to search for a random prime of that size.
The result displays in decimal and hexadecimal. A confidence estimate is shown.
Click "Copy" next to either format to copy the value to your clipboard.
Click "Generate Again" to find a different prime of the same bit length.

Use cases

Generate candidate primes for RSA key pairs during cryptography coursework.
Test primality implementations against known-prime ground truth.
Produce large primes for Diffie-Hellman key exchange prototypes.
Explore how prime density changes across bit lengths.
Benchmark browser BigInt performance on Miller-Rabin iterations.
Demonstrate probabilistic primality testing to students.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu