I think 4000 miles is a lowball number. I read on the navy website that its more like 6000-7000 miles.
I was talking with a submarine officer over a couple of drinks at the O club in Newport many years ago, and we got on the subject of submarine speed. He had just come off a tour on the Scamp, which was a Skipjack class sub and considered to be the fasted subs ever commissioned. I asked him what the top end of the sub was and he gave me the standard Navy answer, "The speed of the Scamp is in excess of 30 knots." Then he paused and said, "But our excess of 30 knotw was higher than any other sub in the Navy." Likewise the listed range of the D5 is in excess of 4000 miles. It's the size of the excess that is the secret.
The unclassified specs for the Trident II D5 list the range at 6000 nautical miles or 6,905 statute miles. I'm not sure where the 4000 miles figure came from, but it's wrong.
Doesn't really matter if the sub is sitting five miles off the enemy's coast!