If you open System Preferences and click on the Time Machine item, and then do a backup, you will see a progress bar and text saying what is going on and an estimate of how much time it's gonna take.
You say 2GB but am guessing you mean 2TB (as 2GB drives haven't been sold for many many years), so is the TM backup 430GB rather then 430MB. I would suspect GB not MB given the state of how large Mac OS is now-days.
Which MacBook Air do you have? Does it have USB3 ports? or does it have a Thunderbolt-to-usb converter or ??? Or is it a thunderbolt-to-USB2 converter or ??? Basically what is the bandwidth between the computer and the disk?
Also look at Activity Monitor and see how much CPU the encryption process is taking ... not sure of the name but would suspect it is the highest cpu process (so sort the list by clicking on the CPU column - and make sure to show all processes (from the View menu).
The encryption process can take a long time the first time but four days does seem a bit excessive.
Look at the ".Backup.log" (yes the file starts with a period) in the folder /Volumes/TMvolume/Backups.backupdb/system-name/snapshot/ (change to fit your TMvolume name and system-name and snapshot name) and see what it says...this file has special permissions so you might need to view it with "sudo more .Backup.log" in a Terminal window with the current directory set to the folder containing the .Backup.log file.
Good luck...