my SGS4 won't update when tap software update

When I try to update my phones OS it flashes the words "checking for updates" on the screen for a few seconds, then says that software updates are currently unavailable, I suspect that the update servers were permanently shut down to make people want a new phone, so I want to update my phone from 4.3 to 4.4 or a little higher than that, but I don't know the best way, (please help, I really want to play pokemon go)

Thanks in advance.