Finding properly ripe peaches

Sometimes, peaches sold at supermarkets seem totally ripe from the outside but are not ripe inside. For example, they may be mostly red outside but green inside. It's possible to check for this by looking into the indentation where the stem is. Unripe peaches tend to have some green there and ripe peaches don't. I suppose some chemical ripening agent (ethylene?) is used to ripen the skin, and that agent doesn't make it deeper into the fruit or into the stem indentation.