They're called rangpur limes, and they are just as orange on the inside:
Although they're called limes, these fruits are actually a very sour mandarin orange. The taste is described to be something between a tangerine and a lemon. To be honest, all I really tasted was the acidity.
So you might be wondering, what did I make with these? Hummus. Yeah, I know it sounds like a weird way to use exotic citrus, but I really wanted hummus and didn't have any lemons around. I ended up using the juice from two of the limes, it gave the hummus a nice citrus flavor. I still have one more, I'm thinking a vinaigrette is in order, maybe with some orange olive oil.