The Plank is one of my favourites and I often employ it as a disciplinary measure at my local cadet unit (corporal punishment is still legal right?)
longest I have seen it held for is 10minutes, longest I have held for is 6minutes 20 something seconds - these times were for a selection for a tall ships race, the plank being a good indicator of mental strength.
On my own, in my room, I am struggling to get past 1.20 so do 4 1 minute intervals with 10-15 mins rest in between. I am still unsure if this is as benefitial as dorsal raises + situps, but the plank certainly does make you think of the phrase "no pain no gain".
I think the most effective core body work outs are situps, dorsal raises (where you lie on your front, hands on head and raise your back off the floor - apologies if dorsal raises is the incorrect name). Another one is to hold a weight (between 2-10kg) with both arms bent about stomach height and twist 90 degrees to the left, then a full 180 degrees so you are facing the right. Repeat as many times as you can within the minute.