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I would never store eggs in this manner, because the texture and flavour degradation will make them unpleasant to eat. However, to actually answer your question--and again, I urge you not to do this because stored and reheated eggs will taste like garbage--cooked eggs should keep for up to 72 hours in the refrigerator.
Do not keep boiled eggs unrefrigerated for more than two hours. Do not keep eggs for more than a week. Boiled eggs only last one week in the refrigerator; raw eggs, on the other hand, can stay fresh in the refrigerator for as much as three to five weeks, depending on the expiration date on the carton. If you detect an unpleasant odor from an egg, whether it's raw or cooked, throw it out.