I've heard that as an egg sits, the yolk slowly descends and as soon as the yolk sits against the shell, it'll go bad. If you keep turning the eggs every week or so, they'll keep for months even at room temperature. I've never tested this, but someone I know found that eggs could last at least 8 weeks this way.

This is the Mother Earth News study that often comes up on Google that fertile eggs, and possibly infertile eggs, could keep as long as 7 months if you refrigerate them and don't wash off their natural coating.