Cut tops off grapefruits, a third of the way down from stem end. Place trimmed bottoms in 8-quart stockpot; cover with 3 quarts water. Cover surface of water directly with a piece of parchment paper cut to same size diameter as the stockpot. Bring to a boil; reduce heat and simmer, uncovered, for 2 hours.
Remove grapefruits; place upside down on a wire rack to drain. Reserve parchment round. When cool enough to handle, scoop out flesh with a spoon (do not puncture grapefruit skin). Discard flesh.
Combine sugar, corn syrup, and 3 3/4 cups water in the stockpot; bring to boil over medium-high heat, using a wet pastry brush to brush down sugar crystals that form on side of pot. Clip candy thermometer to pot; cook until syrup reaches thread stage (230 degrees). Add grapefruit bowls; reduce heat. Cover with reserved parchment round and simmer at least 1 hour, occasionally turning gently. Grapefruits should be unevenly translucent. Turn off heat; let cool in syrup until completely translucent, about 2 hours. Using whisk small enough to fit in bowls, gently lift them from syrup. Place upside down on rack over baking sheet. Let dry overnight. Store in airtight container lined with parchment paper.
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