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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.
Generally, the rule of thumb with all cooked food is that anything will last 5 to 7 days in the fridge at about 45 degrees F. However, if you leave the shells on next time, there will be less doubt on how long boiled eggs will keep because there will have been no exposure to outside bacteria.