randomnumber

A random number is a value selected from a set of possible numbers according to a specified distribution, usually with no predictable pattern. In computing, random numbers are produced by random number generators (RNGs) and are essential for simulations, statistical sampling, randomized algorithms, and testing. RNGs are commonly categorized as true random number generators (TRNGs) or pseudo-random number generators (PRNGs).

TRNGs rely on physical processes, such as electronic noise, radioactive decay, or quantum phenomena, and are not repeatable. PRNGs use deterministic algorithms to produce long sequences of numbers that appear random; given the same initial seed and algorithm, the sequence is repeatable, which aids reproducibility in experiments and software testing. Seeding and state management are important for controlling unpredictability and repeatability.

Common PRNG algorithms include linear congruential generators, Mersenne Twister, xoroshiro/xorshift families, and modern variants like PCG. Many libraries provide cryptographically secure RNGs that aim to resist prediction, often by combining PRNGs with entropy sources and cryptographic primitives. In practice, numbers are typically generated with a uniform distribution over a defined range, and other distributions (normal, exponential) can be derived through transformations.

Key properties of a good random number sequence are uniformity, independence between successive values, and a long period. Quality assessment employs statistical tests for distribution and correlation, and, for cryptographic use, unpredictability and resistance to state compromise.

Applications range from Monte Carlo simulations and randomized algorithms to gaming and software testing. When security is a concern, cryptographic RNGs should be used, with careful attention to entropy sources, seeding, and state protection.