How would you design a Pseudo Random Number Generator (PRNG)?

A Pseudo Random Number Generator (PRNG) produces a sequence of numbers that appear random but are actually generated by a deterministic algorithm. To design one, you'd start with a seed value, which is the initial input. This seed determines the entire sequence. Common PRNG algorithms include Linear Congruential Generators (LCGs), which use a simple mathematical formula: X_{n+1} = (a * X_n + c) mod m, where X_n is the current number, a is the multiplier, c is the increment, and m is the modulus. The choice of a, c, and m is crucial for the quality and period length of the generated sequence. More sophisticated methods like Mersenne Twister offer better statistical properties and longer periods, making them suitable for simulations and cryptography.