5. A simple RNG: linear congruential

Lehmer (1949)

          Xn+1 = (a * Xn + c) mod m

where a, c and m are constants. An example:

Set a=7, c=7 and m=10:

Xn	aXn + c	Xn+1
7	7*7 + 7 = 56	6
6	7*6 + 7 = 49	9
9	7*9 + 7 = 70	0
0	7*0 + 7 = 7	7

This is obviously not a great RNG: it cycles back to the original seed value after just 4 values.

Lewis, Goodman, Miller (1969)

A minimal standard RNG, according to Park and Miller (1988):

     a = 16807
     c = 0
     m = 231-1 = 2147483647

Period: 2³¹-2 = approx 2.1*10⁹

Note that an ordinary Pentium III will exhaust this period in less than one CPU hour!