that really is not very big
i work with 8192x4096 (8k) and 16384x8192 ( 16k ) px images all the time
now a 16k image will lag a bit for me seeing as i only have a i5 cpu and 8 gig ram
-- a mid price range Desktop box from 5 years ago .
gimp holds in memory , by default , 5 undo levels - this DOSE eat up the RAM and can cause the need to use the SWAP on the disk
- you can clear the undos - not the best idea !!!
Or one other way is to work only on parts
crop the upper left 30 % ( some overlap ) then the upper right then the lower right and the lower left
this ram issue is do the use of GTK ( Gimp Tool Kit )
gimp 2.9 and the 2.10 ( should be 3.0 ) are porting the rest to GEGL
Gimp 2.8.14 is still using GTK for a lot of things
you can test you the TESTING and DEVELOPMENT Gimp 2.9
it builds rather easily compared to the LAST development " 2.7 " - 2.7 was a nightmare to build from source
-- linux build ( takes about 10 min.)
http://wiki.gimp.org/wiki/Hacking:Building/Linux
-- windows - using MinGW
http://wiki.gimp.org/wiki/Hacking:Building/Windows
-- windows using MS visual-studio
HA! HA! HA! HA!
i did it ONE time and NEVER AGAIN !!!!
or use the prebuilt
http://nightly.darkrefraction.com/gimp/
lib cairo is causing some issues with BIG paint brushes ( 150+ px. ) in gimp 2.8