Preheat oven to 450 degrees F.
Grease two large baking sheets(or cover with parchment paper).
In a large bowl,sprinkle the yeast over the warm water(water should be very warm to touch).;stir with a rubber spatula until well blended and the yeast is dissolved.
With a wooden spoon, gradually stir in sugar, salt and 3 1/2 cups of flour until a soft and slightly sticky dough forms.
Turn dough onto a well-floured board.To knead fold the dough towards you;with the heels of your hands push the dough away with short rocking motions.Rotate the dough a quarter turn and repeat motion.Continue kneading and turning for about 5-7 minutes,adding another 1/2 cup or more of flour as necessary,until the dough is smooth and elastic.The dough should not stick to your hands or the board.
Cut the dough in half and then cut each half into six equal-sized pieces.With floured hands,roll one piece of dough between the palms of your hands to form a dough rope.Continue rolling and stretching the dough rope until it is 15 inches long.Place the rope on a baking sheet.Cross the left side of the rope over to the middle to create a loop.Then fold the right side of the rope over the left to create a pretzel shape.
Continue with the remaining dough,placing the pretzels three inches apart on the baking sheet.Enlarge holes in pretzels by inserting thumb and index fingers into holes.This will prevent them from completely closing during baking.In a small bowl mix together egg and water,brush on pretzels.Sprinkle with salt.
Bake 15 to 20 minutes or until golden brown.