Random Number Generator

Generate random numbers, sequences, and lists with customizable ranges

Generator Settings

Generated Numbers

What is a Random Number Generator?

A random number generator (RNG) is a computational or physical device designed to generate a sequence of numbers or symbols that lack any pattern, i.e., appear random. Random number generators are essential for various applications including simulations, cryptography, statistical sampling, and games.

Types of Random Number Generators

True Random Number Generators (TRNG):

Based on physical phenomena

  • Atmospheric noise
  • Radioactive decay
  • Thermal noise
  • Quantum phenomena

Pseudorandom Number Generators (PRNG):

Algorithm-based generators

  • Linear congruential generators
  • Mersenne Twister
  • Cryptographic generators
  • Statistical generators

How to Use the Generator

  1. Choose the type of random numbers (integers, decimals, etc.)
  2. Set the minimum and maximum values for your range
  3. Specify how many numbers you want to generate
  4. Choose whether to allow duplicates or not
  5. Click "Generate" to create your random numbers
  6. Copy or download the results as needed

Applications of Random Number Generators

Statistical Sampling:

  • Survey sampling
  • Quality control
  • Research studies
  • Market research

Simulations:

  • Monte Carlo simulations
  • Risk analysis
  • Financial modeling
  • Scientific modeling

Games & Entertainment:

  • Lottery numbers
  • Dice rolls
  • Card shuffling
  • Prize drawings

Random Number Properties

  • Uniformity: Each number in the range has equal probability
  • Independence: Each number is independent of previous numbers
  • Unpredictability: Cannot predict future numbers from past ones
  • Periodicity: For PRNGs, the sequence eventually repeats

Quality of Random Numbers

The quality of random numbers depends on the application:

  • Cryptography: Requires cryptographically secure random numbers
  • Simulations: Need good statistical properties
  • Games: Can use simpler generators
  • Sampling: Requires uniform distribution

Common Random Number Distributions

Uniform Distribution:

All numbers in range have equal probability

U(a,b) where a ≤ x ≤ b

Normal Distribution:

Bell-shaped curve around a mean

N(μ,σ²) with mean μ and variance σ²

Best Practices

  • Use appropriate ranges for your application
  • Consider whether duplicates are acceptable
  • For cryptographic applications, use secure generators
  • Test the randomness if critical for your application
  • Document the generator used for reproducibility