The four-color map problem was proven by Haker and Appel in 1976 which took over a month to do.
Can somebody with a home computer system (say $1,000) be able to do the same today?
Moor's law suggests that computers are 130000 times faster today than in 1976, also the proof has been improved, so there are fewer cases to check. So if you can code it, the computation it self should be easy to do on a modern personal computer.