It depends, A week-old egg is preferable for preparing a hard-cooked egg because the shell is easier to peel. On the other hand, as an egg gets older, its yolk protein molecules gradually lose their binding abilities. This means that fresher eggs are the first choice when frying or poaching because they have a thicker egg white and firmer yolk, qualities that increase the eventual compactness and attractiveness of the cooked egg.
Fresher eggs are also superior when you use the yolk to leaven, thicken, or emulsify a preparation. Moreover, the recently laid egg is easier to separate because as an egg ages, the membrane of its yolk weakens. Finally an egg fresh from the coop has more flavor and nutritional value.
For the record, the egg nestled in a box in the supermarket display case is usually three to ten days old, though, two or three week-old eggs are not rare in municipalities that do not require open dating. Some firms extend the storage life of their eggs to six months by coating the shells with a light mineral oil that helps keep harmful bacteria out and beneficial moisture and carbon dioxide in. Another method of giving whole eggs super-longevity is storing them in carbon dioxide chambers.
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