RANDU is a linear congruential pseudorandom number generator (LCG) of the Park–Miller type, which was used primarily in the 1960s and 1970s. It is defined by the recurrence:

${\displaystyle V_{j+1}=65539\cdot V_{j}\,{\bmod {\,}}2^{31}\,}$

with the initial seed number, ${\displaystyle V_{0}}$ as an odd number. It generates pseudorandom integers ${\displaystyle V_{j}}$ which are uniformly distributed in the interval [1, 2³¹ − 1], but in practical applications are often mapped into pseudorandom rationals ${\displaystyle X_{j}}$ in the interval (0, 1), by the formula:

${\displaystyle X_{j}={\frac {V_{j}}{2^{31}}}}$.

IBM's RANDU is widely considered to be one of the most ill-conceived random number generators ever designed, and was described as "truly horrible" by Donald Knuth. It fails the spectral test badly for dimensions greater than 2 as will be seen below.

The reason for choosing these particular values for the multiplier and modulus had been that with a 32-bit-integer word size, the arithmetic of mod 2³¹ and ${\displaystyle 65539}$ ${\displaystyle ({\text{i.e., }}2^{16}+3)}$ calculations could be done quickly, using bitwise operators in hardware, but the values were chosen for computational convenience, not statistical quality.