Even the best vacuum pumps cannot lower the pressure in a container below 10^(−15) atm.? how many molecules of air are left in each cubic centimeter in this "vacuum? " assume that the temperature is 276 k .

You can rewrite the ideal gas as n/V=P/RT to find the moles per liter.
10^(-15)atm/(0.08206Latm/molK)(276K)=4.415x10^(-17)mol/L

since we know that one cm³ equals 1mL which equals .001L you can turn the mol/L into mol/cm³.
(4.415x10^-17mol/L)x(1L/1000mL)=4.415x10^(-20)mol/cm³

than multiply that number by Avogadro's number to find the number of molecule in that unit volume.
(4.415x10^(-20)mol/cm³)x(6.02x10^23molecules/mole) 
=2.658x10^4molecules/cm³

I hope this helps

Temperature and pressure