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RANDU is a linear congruential pseudorandom number generator of the Park–Miller type, which has been used since the 1960s. It is defined by the recurrence:

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

with the initial seed number, $\scriptstyle V_0$ as an odd number. It generates pseudorandom integers $\scriptstyle V_j$ which are uniformly distributed in the interval , but in practical applications are often mapped into pseudorandom rationals $\scriptstyle X_j$ in the interval , by the formula:

$$X_j = \frac{V_{j}}{2^{31}}$$

IBM's RANDU is widely considered to be one of the most ill-conceived random number generators ever designed. It fails the spectral test badly for dimensions greater than 2, and every integer result is odd. However, at least eight low-order bits are dropped when converted to single-precision (32 bit, 24 bit mantissa) floating-point.

The reason for choosing these particular values is that with a 32-bit-integer word size, the arithmetic of mod 2 and 65539 (i.e., 2 + 3) calculations could be done quickly, using special features of some computer hardware.