An integer's PD's (Proper Divisors) are all those integers less than itself which divided into it exactly.
An Abundant Number is one which is less than the sum of its PD's.
A Deficient Number is one which is greater than the sum of its PD's.
A Primitive Abundant Number is an Abundant Number whose PD's are all Deficient Numbers.
Example: 20 is Abundant because the sum of its PD's is 1+2+4+5+10 = 22. All the PD's are themselves Deficient Numbers. Thus, 20 is a Primitive Abundant Number.
What is the smallest interval between two successive Primitive Abundant Numbers less than 10,000?