I break an egg directly into the pot of boiling water when there's about 2.5 to 3 minutes left on the noodles' recommended cooking time. This usually gets the whites solid and leaves the yolk runny in the middle.

I'm not a food expert though. This might be unsafe. I've done it a lot though and haven't gotten sick.

4 minutes would probably cook the yolk all the way through if you want a solid yolk.