I'm proud of this one...?

Euler is getting ready to cut some pie for his mathematician houseguests. Fermat suggests cutting the pie such that the angles (in degrees) of the slices form the sequence of prime numbers. Heaviside further suggests that each person in the room will get one slice of pie. If the pie has a radius of 1 ft (yes, mathematicians love pie), what is the area of the slice that will be left over from cutting the pie in this fashion and how many mathematicians are in the room?