pseudorandomnumber

A pseudorandom number is a value produced by a deterministic algorithm that imitates randomness. The sequence depends on an initial seed and internal state and will eventually repeat with a finite period, though it can be made to pass many statistical tests and appear uniform to observers.

Most pseudorandom number generators (PRNGs) rely on a recurrence relation modulo a large modulus, producing a stream of numbers that can be mapped to a uniform distribution in [0,1) or to integer ranges. Notable families include linear congruential generators, Xorshift, and the Mersenne Twister. The seed controls the entire sequence, making the output reproducible for testing and debugging.

PRNGs offer speed, reproducibility, and broad applicability in simulations, randomized algorithms, and procedural content generation. However, they are not truly random and can be predictable if the internal state or seed is known. For security-sensitive tasks, cryptographically secure PRNGs (CSPRNGs) or true entropy sources should be used. CSPRNGs are built from cryptographic primitives and are designed to resist state inversion and prediction, albeit with typically higher computational cost.

Historically, the concept arose in the mid-20th century with early linear congruential methods, such as Lehmer’s generator. Modern libraries popularized the Mersenne Twister and its successors, which provide long periods and good statistical properties for general-purpose use. The term pseudorandom number reflects that the numbers are deterministic yet intended to approximate the behavior of true randomness for practical applications.