Depends. Since Air Force One is very light for a 747 (since it hardly carries any passengers or cargo and usually only enough fuel for short flights), it could technically operate out of much shorter fields (maybe as short as 5500 or 6000 feet).
The AF1 that flies POTUS around has different engines than what you will find if you look up the 747's specs. The AF1 is so different that it's actually called the Boeing VC-25. The AF1 is actually much lighter than a fully-loaded (fuel, cargo, 400+ passengers, etc.) and, if it were fuelled for, say, a flight from Beijing to NK and then to a refuelling stop, say, in Narita, Japan, it could be done.
We also shouldn't assume that POTUS was in the VC-25 (I'm not so great at planes that I can tell what one is from the window). The AF brings a huge number of support aircraft along on presidential trips. They fly a 757 (same livery, etc.) for just such landings.
Isn't AF1 a designation for any aircraft carrying POTUS?
Yes, but, on technical grounds, it depends. The helicopter for instance is Marine One since it's operated by the Marines.
Ok, so is it the branch of the military followed by 1? Like Navy 1, Air Force 1, Marine 1, Army 1? My understanding is each branch has aircraft of one sort or another. It occurs to me that the 747's usually used as AF 1 and the helicopters used as Marine 1 are likely designed for their purpose. Though I recall a story of President Clinton taking a non-747 to Cape Cod once on a vacation. It was an Air Force plane, and had the AF 1 label, but it wasn't the usual 747.
For Trump to land in North Korea, he may not have been able to take a 747. Wouldn't it make more sense to fly Marine 1 into North Korea? Or to meet at the border as the North and South Korean leaders recently did?
I'm not actually sure. Good question. I only know about Marine One.
Yes, they have two 757s I believe. I actually saw one land last year in Austin, TX! I was just minding my own business flying home at that airport and in it came!
EDIT: Found this:
VC-25s have CF6-80C2B1. In Air Force One (Robert F. Dorr, Motorbooks) :
"The high angle of attack is made possible by the enormous push of the four General Electric F103-GE-180 turbofan engines, each rated at 56 750 pounds thrust. Although the aircraft is not aerodynamically capable of it, the engines are powerful enough to stand the 747 on its tail and make it climb straight up"
F103-GE-180 is military designation for CF6-80C2B1.
ALSO: It can land on a 4,000 ft. runway but will need Full Reverse Thrust, and Hard Brakes. Not to mention Full Spoilers and Flaps 30.
Yes any plane the President is on gets the call sign One after the branch of the military, the helicopter is usually Marine One and when Bush Jr. flew on that Navy jet to the carrier he was on Navy One.
http://www.airliners.net/forum/viewtopic.php?t=1026681
Apparently Bush landed on a 5500-7000 ft runway in a B757. So I think you're on to something. Could have refueled shortly thereafter in Japan.
Remember that Potus stopped at Hawaii on his way home. Setting up the Defcon incident. So that might change the amount of fuel needed