Commodore BasicBASIC 2.0, 339 bytes

In order to get lower-case hex digits, this program is written in "shifted mode" (press <SHIFT>+<C=>)

1k=65535:a=0
2fOb=0tok:fOc=0tok:fOd=0tok:fOe=0tok:fOf=0tok:fOg=0tok:fOh=0tok
3x=a:goS6:?":";:x=b:goS6:?":";:x=c:goS6:?":";:x=d:goS6:?":";:x=e:goS6:?":";:x=f
4goS6:?":";:x=g:goS6:?":";:x=h:goS6:?
5nE:nE:nE:nE:nE:nE:nE:nE:a=a+1:ifa<65536tH2
6y=x/4096:goS7:y=x/256aN15:goS7:y=x/16aN15:goS7:y=xaN15:goS7:reT
7?mI("0123456789abcdef",y+1,1);:reT

Simply making this work on the Commodore 64 was a challenge, because of memory, screen size, data size, and other limitations. I considered implementing the abbreviated representation, but other limitations (such as the undocumented inability to use array elements as loop indices) meant it would increase the length of the program by an estimated 1000 bytes.

Line 7 is an implementation of HEX$(), which Commodore BasicBASIC 2.0 is lacking. I can't use a DEF FN for this because those can only return numbers, not strings. Line 6 is a subroutine that applies it to a group of four digits, which would have been considerably shorter if functions could return strings.

Lines 2 and 5 are eight nested loops, implemented as seven "for" loops and a conditional goto because eight "for" loops, when combined with the two "gosubs" for printing out the address, will overflow the C64's tiny stack.

A C64 can print out about 1.2 addresses per second, for an estimated runtime of 1.3*10^31 years.