Prime Number Generator
Generate the first N prime numbers or list all primes inside a custom range. Includes prime count, largest prime, total sum, average prime gap, and twin-prime pair count for quick number-theory exploration.
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Random Number Generator
Generate random numbers using three statistical distributions — Integer (discrete uniform), Float (continuous uniform), and Normal (Gaussian bell curve). Supports seeded output for reproducibility, no-duplicates mode, sort order, and instant statistics including mean, median, standard deviation, and mode.
What Is a Random Number Generator?
A random number generator (RNG) produces sequences of numbers that lack any predictable pattern. This tool uses a seeded Linear Congruential Generator (LCG) — a fast, deterministic pseudo-random algorithm used in programming languages and simulation software worldwide. It supports three distinct statistical distributions for different use cases.
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Integer Mode
Roll dice, pick lottery numbers, generate random IDs, shuffle lists, or run randomised trials.
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Float (Uniform)
Probability simulations, Monte Carlo methods, random sampling from a continuous range.
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Normal (Gaussian)
Model real-world measurements, simulate test scores, generate synthetic data following a bell curve.
How to Use This Generator
- 1Choose a DistributionInteger for whole numbers, Float for decimals spread uniformly across a range, Normal for bell-curve distributed values.
- 2Set Count & RangeEnter how many numbers to generate (up to 10,000) and the minimum/maximum bounds. For Normal mode, set the mean and standard deviation instead.
- 3Configure OptionsChoose decimal places (float mode), a sort order, and whether duplicates are allowed (integer mode). Toggle a fixed seed for reproducible output.
- 4Generate & CopyClick Generate Numbers. Results appear instantly with all values displayed as chips. Click Copy All to grab the full list as a comma-separated string.
- 5Review StatisticsA statistics panel shows count, min, max, sum, mean, median, standard deviation, and mode — instantly useful for data analysis.
How the Distributions Work
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Integer (Uniform Discrete)
Each integer in the range [min, max] has an equal probability of being selected. Formula: value = min + floor(rng() × (max − min + 1))
Example: Rolling a standard die — 6 integers [1, 6], each with exactly 1/6 probability.
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Uniform Float (Continuous)
Every value in [min, max) is equally likely. Used in probability simulations and Monte Carlo integration. Formula: value = min + rng() × (max − min)
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Normal / Gaussian Distribution
Uses the Box-Muller transform to convert two uniform random numbers into normally-distributed values. The result clusters around the mean (μ) with spread controlled by standard deviation (σ).
Z = √(−2 ln U₁) × cos(2π U₂) then X = μ + σZ
68% of values fall within μ ± 1σ | 95% within μ ± 2σ | 99.7% within μ ± 3σ
Worked Examples
① Lottery Quick Pick — 6 unique integers from 1 to 49
Settings: Distribution = Integer, Count = 6, Min = 1, Max = 49, No duplicates = ✓, Sort = Ascending
71423313847
② Monte Carlo π Estimation
Generate pairs of uniform floats in [0, 1] and check if x² + y² ≤ 1 (inside the unit circle). The ratio of interior points × 4 approximates π. With 10,000 pairs this typically gives π ≈ 3.14 ± 0.01.
③ Simulate Test Scores — Normal distribution μ=70, σ=12
Settings: Distribution = Normal, Count = 100, Mean = 70, Std Dev = 12. Expected result: ~68 scores between 58–82, ~95 between 46–94, mean ≈ 70.
Within μ ± 1σ
~68 scores
58 – 82
Within μ ± 2σ
~95 scores
46 – 94
Within μ ± 3σ
~99.7 scores
34 – 106
Frequently Asked Questions
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Explore This Tool in Context
Random Number Generator is part of the Math & Statistics Calculators collection. If you want a broader view of similar workflows, open the Math & Statistics Calculators category page or browse all QuickTools categories.
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