I'm not sure how to do random numbers, but here's a way to just have it count up constantly.
You're gonna want an oscillator and some counters, plus a 7-seg led driver. I don't know part numbers for these offhand, but you could have the oscillator connected to every digit of the display, and for the 10's digit you divide the clock by 10 (with a 4017), then for the 100's digit you divide it by 100 (by 10 twice) and so on.
You could also do it with microcontrollers.