Shell eggs and cut tops and bottoms off with a sharp knife dipped in cold water. Carefully remove yolks from broad end of eggs, being careful not to split whites. Mash yolks to a smooth paste with 4 anchovy fillets, mayonnaise and paprika. Season with salt and freshly ground black pepper, and stuff eggs with this mixture. If mixture is too stiff, add more mayonnaise.
To serve: place egg