I love the thought of a "rare" egg! I believe if you want to make sure they are hard boiled, it's best to heat the water in the pan from cold, don't add boiled water to the pan. I think 5 minutes would probably do it, but I'd leave them for 7-8. Just don't do as I once did, put the eggs on then get involved in a film. I remembered I was boiling eggs when I heard them explode in the kitchen. The pan had boiled dry. I couldn't get rid of the smell for days.