Choose from multiple pseudorandom number generation algorithms with deterministic seeding capabilities for reproducible results.
Welcome to the random number generator. Select an algorithm to begin.
Current seed: Not set
Results
Distribution Visualization
This histogram shows the distribution of your generated numbers. In a good random distribution, you should see a roughly even spread across the range for uniform random numbers. This visual representation can help you understand if your random numbers are behaving as expected.
Generation History
Frequently Asked Questions (FAQ)
What is a pseudorandom number?
A pseudorandom number is a number that appears to be random but is generated using a deterministic algorithm. Unlike true randomness, which comes from unpredictable physical phenomena, pseudorandom numbers are produced by mathematical formulas or algorithms. These numbers are sufficient for most applications but can be reproduced if the starting conditions (seed) are known.
How do computers generate pseudorandom numbers?
Computers are inherently deterministic machines, meaning they follow predictable processes. To generate pseudorandom numbers, they rely on algorithms called pseudorandom number generators (PRNGs). PRNGs start with an initial value, called a seed, and use it to produce a sequence of numbers that mimic randomness. For example, algorithms like Mulberry32 or Xoshiro128** are optimized for generating high-quality pseudorandom sequences efficiently.
Why does the seed matter?
The seed acts as the starting point for a PRNG. If the same seed is used, the PRNG will always generate the same sequence of numbers, making the process deterministic. This is particularly useful for debugging, simulations, or any scenario where reproducibility is important. If no seed is provided, many generators use the current time to ensure each sequence is unique.
What is determinism in computing?
Determinism in computing means that given the same inputs, a system will always produce the same outputs. PRNGs are deterministic by design, which is why setting the same seed guarantees the same sequence of pseudorandom numbers. While this predictability is useful in many contexts, it’s also why pseudorandom numbers differ from true randomness.
What are the differences between true random and pseudorandom numbers?
True random numbers are generated from physical processes like radioactive decay or atmospheric noise, which are inherently unpredictable. In contrast, pseudorandom numbers are calculated using algorithms, making them predictable if the seed is known. True randomness is necessary for applications like cryptography, while pseudorandom numbers are sufficient for simulations, games, and most general purposes.
Which PRNG algorithm should I use?
The choice of PRNG depends on your needs:
- Math.random(): Quick and sufficient for simple tasks but not seedable. Suitable for lightweight applications like randomizing UI elements or simple games.
- Mulberry32: Fast and efficient, suitable for most general-purpose applications. Offers deterministic results when seeded, making it a great choice for simulations or debugging.
- Xoshiro128**: A modern, high-quality PRNG with excellent statistical properties, ideal for simulations, complex games, or applications that require a long period and high randomness quality.
- PCG (Permuted Congruential Generator): A newer, lightweight PRNG designed for excellent randomness quality with minimal overhead. Perfect for general-purpose tasks, especially when computational efficiency is a priority.
- Mersenne Twister: Known for its extremely long period (\(2^{19937}-1\)) and high-quality randomness. Best for scientific simulations, numerical computations, or any scenario requiring high precision and long sequences.
- SplitMix64: A simple generator often used for initializing other stateful PRNGs like Xoshiro128**. Great as a seed generator or for lightweight applications.
- Blum Blum Shub: A cryptographically secure PRNG that relies on number-theoretic principles. Best suited for cryptographic applications where unpredictability is critical.
- ISAAC (Indirection, Shift, Accumulate, Add, and Count): Designed for cryptographic applications, this PRNG is both secure and fast, making it a good choice for sensitive randomness needs.
What are PRNGs used for?
Pseudorandom Number Generators (PRNGs) are used in a wide range of applications where randomness or unpredictability is required. Common use cases include:
- Simulations: Generating random data for scientific models, such as Monte Carlo simulations.
- Games: Randomizing elements like loot drops, enemy behavior, or procedural content generation.
- Testing: Creating randomized test cases to validate algorithms or systems under diverse conditions.
- Data Security: Providing entropy for cryptographic systems (when combined with secure generators).
- Machine Learning: Shuffling datasets, initializing weights in neural networks, or sampling data.
- Statistical Sampling: Selecting random subsets of data for analysis or surveys.
What is the difference between a PRNG and a TRNG?
The key difference lies in how the randomness is generated:
- Pseudorandom Number Generator (PRNG): A PRNG uses deterministic algorithms to produce sequences of numbers that appear random. Given the same seed, a PRNG will always generate the same sequence. Examples include Xoshiro128** and Mulberry32.
- True Random Number Generator (TRNG): A TRNG relies on physical phenomena, such as radioactive decay, thermal noise, or atmospheric noise, to generate randomness. These processes are inherently unpredictable and cannot be reproduced.
Use Cases:
- PRNGs are commonly used for simulations, games, and applications where controlled randomness is beneficial.
- TRNGs are critical for cryptography and high-security systems where unpredictability is essential.
How to Test the Quality of a PRNG
To ensure the reliability and security of a Pseudorandom Number Generator (PRNG), it's crucial to subject it to rigorous testing. Here are some common methods:
Statistical Tests:
- Chi-Square Test: Evaluates whether the observed frequency distribution of the generated numbers matches the expected distribution (usually uniform).
- Kolmogorov-Smirnov Test: Compares the empirical cumulative distribution function (ECDF) of the generated numbers to a theoretical distribution (e.g., uniform or normal).
- Autocorrelation Test: Examines the correlation between numbers at different lags to assess the independence of the generated sequence.
Comprehensive Test Suites:
- Diehard Tests: A comprehensive suite of statistical tests for randomness, including tests for uniformity, independence, and other statistical properties.
- TestU01: Another powerful test suite that offers a wide range of statistical tests for evaluating PRNGs.
- NIST Statistical Test Suite: Provides a variety of statistical tests to assess the randomness of bit sequences.
Visual Analysis:
- Histogram: Visualizes the frequency distribution of the generated numbers. A uniform distribution is expected for a good PRNG.
- Scatter Plot: Plots pairs of consecutive numbers to identify any patterns or correlations. A random sequence should not exhibit any discernible patterns.
Entropy Calculation:
Measures the randomness of a sequence of bits. A higher entropy value indicates greater randomness.
Additional Considerations:
- Seed Sensitivity: A good PRNG should be sensitive to the initial seed value, producing significantly different sequences for different seeds.
- Period Length: A long period ensures that the PRNG won't repeat itself for a long time.
- Statistical Independence: The generated numbers should be independent of each other.
- Uniform Distribution: The numbers should be uniformly distributed across the desired range.
By employing these testing methods and considering the aforementioned factors, you can assess the quality of a PRNG and ensure its suitability for various applications.
What are the security implications of PRNG?
PRNGs have significant security implications, especially in cryptographic applications:
- Predictability: PRNGs are deterministic, meaning that if the seed is known or guessed, the entire sequence can be reproduced. This makes insecure PRNGs unsuitable for cryptographic purposes.
- Seed Exposure: If an attacker gains access to the seed, they can predict all future (and past) outputs of the PRNG.
- Weak Algorithms: Using outdated or low-quality PRNGs can lead to vulnerabilities, as attackers might exploit patterns or statistical biases in the generated numbers.
Mitigation: For secure applications, use Cryptographically Secure PRNGs (CSPRNGs) like those provided by libraries or APIs such as the Web Crypto API or OpenSSL.
PRNGs are powerful tools, but their misuse in security-critical contexts can lead to significant risks.What does "allow repeats" mean?
If "allow repeats" is checked, the generator can produce the same number multiple times in the output. If unchecked, the generator will ensure all numbers in the output are unique. Note that if the range is too small to produce the desired quantity of unique numbers, the generator will show an error.
What does the "sort results" option do?
The "sort results" option arranges the generated numbers in ascending order. This does not affect the randomness of the generated sequence but can make it easier to read or use the output in contexts where sorted data is required.
Can I use this generator for cryptographic purposes?
No, this generator is not suitable for cryptographic purposes. Cryptographic applications require secure random number generators (CSPRNGs) that are designed to be unpredictable even if the algorithm or seed is known. Examples of secure generators include algorithms based on system entropy or specialized libraries like the Web Crypto API.
Why does this generator initialize with the current time?
If you don't provide a seed, the generator uses the current time as the seed to ensure that each run produces a unique sequence of numbers. This approach is a common fallback for PRNGs to guarantee non-repeating sequences in most practical applications.
Random Number Generation in Popular Languages
Random number generation is a common requirement in various programming scenarios, from simulations to games. Below are examples of how to generate random numbers in Python, R, JavaScript, and Java.
Random Number Generation in Python
Python provides the random module for generating random numbers. Below is an example without setting a seed:
import random
# Generate a random float between 0 and 1
random_float = random.random()
print("Random Float:", random_float)
# Generate a random integer between 1 and 100
random_int = random.randint(1, 100)
print("Random Integer:", random_int)
# Generate a random number from a uniform distribution
random_uniform = random.uniform(10, 20)
print("Random Uniform:", random_uniform)
# Choose a random element from a list
random_choice = random.choice(['apple', 'banana', 'cherry'])
print("Random Choice:", random_choice)Note the seed is not set in this example, so your random values may differ.
Random Integer: 5
Random Uniform: 13.097440459401195
Random Choice: apple
Setting a Seed for Deterministic Output
By setting a seed, you can make the random number generator deterministic, ensuring the same random values are generated every time. Here's an example:
import random
# Set a seed for reproducibility
random.seed(42)
# Generate a random float between 0 and 1
random_float = random.random()
print("Random Float:", random_float)
# Generate a random integer between 1 and 100
random_int = random.randint(1, 100)
print("Random Integer:", random_int)
# Generate a random number from a uniform distribution
random_uniform = random.uniform(10, 20)
print("Random Uniform:", random_uniform)
# Choose a random element from a list
random_choice = random.choice(['apple', 'banana', 'cherry'])
print("Random Choice:", random_choice)When the seed is set, the output remains consistent:
Random Integer: 4
Random Uniform: 17.41550499759833
Random Choice: apple
Random Number Generation in R
R provides functions like runif for generating uniform random numbers and rnorm for normal distributions. Below is an example without setting a seed:
# Generate 1 random number between 0 and 1
random_number <- runif(1)
print(random_number)
# Generate 5 random integers between 1 and 100
random_integers <- sample(1:100, 5, replace = TRUE)
print(random_integers)
# Generate random numbers from a normal distribution
random_normal <- rnorm(5, mean = 0, sd = 1)
print(random_normal)Note the seed is not set in this example, so your random values may differ.
[1] 83 53 95 35 47
[1] 1.77511090 -0.09114364 -0.83494517 -0.09144749 0.22572456
Setting a Seed for Deterministic Output
By setting a seed using the set.seed function, you can ensure that the random number generator produces consistent output.
For a more detailed explanation, check out
Understanding set.seed() in R: A Comprehensive Guide
.
# Set a seed for reproducibility
set.seed(42)
# Generate 1 random number between 0 and 1
random_number <- runif(1)
print(random_number)
# Generate 5 random integers between 1 and 100
random_integers <- sample(1:100, 5, replace = TRUE)
print(random_integers)
# Generate random numbers from a normal distribution
random_normal <- rnorm(5, mean = 0, sd = 1)
print(random_normal)When the seed is set, the output remains consistent:
[1] 65 25 74 100 18
[1] -1.1045994 0.5390238 0.5802063 -0.6575028 1.5548955
Random Number Generation in JavaScript
JavaScript provides the Math.random() function for generating random numbers. Below is an example without setting a seed:
// Generate a random float between 0 and 1
let randomFloat = Math.random();
console.log("Random Float:", randomFloat);
// Generate a random integer between 1 and 100
let randomInt = Math.floor(Math.random() * 100) + 1;
console.log("Random Integer:", randomInt);
// Generate a random number in a range
let randomInRange = Math.random() * (20 - 10) + 10;
console.log("Random Number in Range:", randomInRange);
// Pick a random element from an array
let randomChoice = ['apple', 'banana', 'cherry'][Math.floor(Math.random() * 3)];
console.log("Random Choice:", randomChoice);
Since Math.random() is non-seeded, the results will vary each time you run the code.
Random Integer: 8
Random Number in Range: 15.188915202385008
Random Choice: banana
Using Mulberry32 for Seeded Random Numbers
To achieve reproducibility, you can use a seeded pseudorandom number generator like Mulberry32. Here's an example:
// Define the Mulberry32 function
function mulberry32(seed) {
let state = seed >>> 0; // Ensure seed is a 32-bit unsigned integer
return function () {
state = (state + 0x6D2B79F5) | 0;
let t = Math.imul(state ^ (state >>> 15), 1 | state);
t = (t + Math.imul(t ^ (t >>> 7), 61 | t)) ^ t;
return ((t ^ (t >>> 14)) >>> 0) / 4294967296;
};
}
// Create a seeded random number generator
const seededRandom = mulberry32(42);
// Generate random numbers using the seeded generator
let randomFloat = seededRandom();
console.log("Random Float:", randomFloat);
let randomInt = Math.floor(seededRandom() * 100) + 1;
console.log("Random Integer:", randomInt);
let randomInRange = seededRandom() * (20 - 10) + 10;
console.log("Random Number in Range:", randomInRange);
let randomChoice = ['apple', 'banana', 'cherry'][Math.floor(seededRandom() * 3)];
console.log("Random Choice:", randomChoice);
When using Mulberry32 with a fixed seed, the results remain consistent:
VM704:20 Random Integer: 45
VM704:23 Random Number in Range: 18.5246579349041
VM704:26 Random Choice: cherry
Random Number Generation in Java
Java provides the java.util.Random class and methods in the Math library for random number generation. Below is an example without setting a seed:
import java.util.Random;
public class RandomExample {
public static void main(String[] args) {
Random random = new Random();
// Generate a random float between 0 and 1
float randomFloat = random.nextFloat();
System.out.println("Random Float: " + randomFloat);
// Generate a random integer between 1 and 100
int randomInt = random.nextInt(100) + 1;
System.out.println("Random Integer: " + randomInt);
// Generate a random number in a range
double randomInRange = 10 + (20 - 10) * random.nextDouble();
System.out.println("Random Number in Range: " + randomInRange);
// Generate a random boolean
boolean randomBoolean = random.nextBoolean();
System.out.println("Random Boolean: " + randomBoolean);
}
}Since no seed is set, the output will vary each time you run the program.
Random Integer: 15
Random Number in Range: 18.566926130188133
Random Boolean: false
Setting a Seed for Deterministic Output
By setting a seed for the Random object, you can ensure that the random number generator produces the same sequence of random numbers every time. Here's an example:
import java.util.Random;
public class SeededRandomExample {
public static void main(String[] args) {
// Create a Random object with a fixed seed
Random random = new Random(42);
// Generate a random float between 0 and 1
float randomFloat = random.nextFloat();
System.out.println("Random Float: " + randomFloat);
// Generate a random integer between 1 and 100
int randomInt = random.nextInt(100) + 1;
System.out.println("Random Integer: " + randomInt);
// Generate a random number in a range
double randomInRange = 10 + (20 - 10) * random.nextDouble();
System.out.println("Random Number in Range: " + randomInRange);
// Generate a random boolean
boolean randomBoolean = random.nextBoolean();
System.out.println("Random Boolean: " + randomBoolean);
}
}When using a fixed seed, the output remains consistent:
Random Integer: 64
Random Number in Range: 16.832234717598453
Random Boolean: false
Further Reading
To explore more about random number generation, PRNGs, and related topics, check out the following resources:
- Random Number Generation (Wikipedia) - A comprehensive overview of random number generation techniques and applications.
-
Python Random Module Documentation
- Official Python documentation for the
randommodule. -
V8 JavaScript Engine
- Understand how JavaScript's
Math.random()is implemented in popular JavaScript engines like V8. - L'Ecuyer, Pierre: "Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators" - A seminal paper discussing well-performing multiple recursive generators.
- Matsumoto and Nishimura: "Mersenne Twister: A 623-dimensionally Equidistributed Uniform Pseudo-Random Number Generator" - The original paper introducing the widely used Mersenne Twister PRNG.
- Blackman, David and Vigna, Sebastiano: "Scrambled Linear Pseudorandom Number Generators" - proposes a novel approach to improve the statistical quality of PRNGs by combining linear transformations with nonlinear scrambling functions, addressing the limitations of traditional LFSRs.
- xoshiro/xoroshiro generators and the PRNG shootout - Describes PRNGs implemented by David Blackman and Sebastiano Vigna
- Extensive List of PRNG Research Preprints, Journals, and Proceedings
Attribution and Citation
If you found this guide and tools helpful, feel free to link back to this page or cite it in your work!
Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.