In a large pot, arrange the eggs in a single layer and add enough water to cover. Bring to a boil over high heat, then cover and remove from the heat; let stand for 10 minutes. Drain, then cover the eggs with ice water. Let stand until cool to the touch.
Peel the eggs, halve lengthwise and scoop the yolks into a medium bowl, reserving the egg whites. Mash the yolks with the mayonnaise, mustard and cayenne; season with salt and black pepper. Spoon the yolk mixture into the egg white halves and dust with paprika.