Nope. i386 and i686 stat for 32-bit. Your kernel is 32-bit. There is a chance you're running a 32-bit OS on a 64-bit architecture, since you can do it without any problem. To check if your CPU is 64-bit, look at the output of
in the flags section you have to look for lm
(= long mode). If you see it, the CPU is 64-bit, if you don't see it the CPU is 32-bit. Anyway, you're running a 32-bit OS otherwise you should see x86_64
from the output of uname -a.