Is the vein in shrimp poop?

Online Answer
Although removing that string is called deveining, it is actually not a vein (in the circulatory sense.) It is the shrimp's digestive tract, and its dark color means it is filled with grit.
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The "white vein" on the inner crescent side of the shrimp is the blood vessel. It's white, rather than red, because the blood of shrimp is clear. There's no food-safety reason to remove this one, but you can if it seems more appetizing to you..