Random Number Generator

How are random numbers generated?

Behind the numbers sits JavaScript's Math.random(), which returns uniformly distributed pseudo-random values. Tick the "no repetition" option and the Fisher-Yates shuffle takes over, making sure each number comes out just once.

Everything is computed inside your own browser.

Pseudo-random vs truly random: what the computer actually does

Computers cannot produce true randomness from arithmetic alone. What we call "random numbers" in software almost always comes from a pseudo-random number generator (PRNG) — a deterministic algorithm that, given an initial seed, produces a long sequence of values that looks statistically random. JavaScript's Math.random() is a PRNG: in V8 it implements xorshift128+; older engines used Mersenne Twister. The output passes most uniformity tests but is fully reproducible if you know the seed and the algorithm.

A truly random number generator (TRNG), by contrast, harvests entropy from physical phenomena: thermal noise in a resistor, photon arrival times, radioactive decay, atmospheric noise (the source random.org famously uses), or the quantum behavior of vacuum fluctuations. The browser exposes a hybrid via crypto.getRandomValues() — a cryptographically-secure PRNG (CSPRNG) reseeded from the operating system's entropy pool (/dev/urandom on Unix, CryptGenRandom on Windows). For lotteries, key generation, salts, tokens, and anything where predictability is a security flaw, always use the Web Crypto API.

Famous PRNG algorithms

• Linear Congruential Generator (LCG) — the classic x_{n+1} = (a·x_n + c) mod m; fast but easily reverse-engineered.
• Mersenne Twister (MT19937) — period of 2^19937−1, the default in Python, R, and MATLAB for decades.
• Xorshift / xoshiro / xoroshiro — Marsaglia's family of bit-shifting generators; small state, excellent speed.
• PCG (Permuted Congruential Generator) — modern LCG variant with permutation output; good statistical quality at low cost.
• ChaCha20 / Fortuna — cryptographic generators used inside CSPRNGs.

Distributions: not all randomness is uniform

PRNGs natively output uniform values in [0,1). Real-world simulations often need other shapes: Gaussian (normal) via the Box-Muller transform, exponential via inverse CDF, Poisson for arrival counts, binomial for coin-flip sums. To get an integer in [min, max], the standard idiom is:

Math.floor(Math.random() * (max - min + 1)) + min

The modulo bias pitfall

A frequent mistake when using crypto.getRandomValues() is reducing a 32-bit integer with % n. If n does not divide 2^32 evenly, some outputs become slightly more likely than others — invisible for n=6, catastrophic for cryptographic ranges. The fix is rejection sampling: discard samples that fall outside the largest multiple of n below 2^32 and draw again.

Standards and use cases

• NIST SP 800-90A/B/C — the U.S. specification for deterministic and entropy-based random generators.
• Public draws — require a CSPRNG plus auditable logs (or an externally-witnessed source like random.org's HMAC API).
• Monte Carlo simulation — Mersenne Twister or PCG are standard for Monte Carlo and statistical sampling.
• Games — Math.random() is fine for dice, loot, shuffling cards in casual play.
• Cryptography — never use Math.random() for keys, salts, IVs, or tokens; always CSPRNG.

FAQ

Is this generator fair for a public raffle? It uses Math.random(), which is statistically uniform but deterministic. For informal raffles it is fine; for prize draws with legal value, use a CSPRNG and keep an auditable record of seed, time, and result.

Are the results reproducible? Not from this tool — every call uses fresh internal state. A seedable Mersenne Twister (via libraries like random-js) would let you replay the same sequence given a seed.

Can I avoid duplicates? Yes — enable the "unique" option. Internally the generator either shuffles a range and slices N values, or rejects repeats with a Set. Note that uniqueness requires quantity ≤ (max − min + 1).

What is "atmospheric noise"? random.org samples electromagnetic background noise picked up by tuned radios. Because it is driven by physical phenomena, the output is non-deterministic in a way no algorithm can match — closer to a TRNG than a PRNG.