I m not sure about its proof but sending example according to this statement.
Example : Factors of 273 = 13 * 7 * 3
In these factors 13 and 7 are prime numbers
So pd(273) = 13 - 7 = 6
This would help you better Finding Factors of Numbers
For a composite positive integer x, denote by pd(x)the smallest positive difference between any two prime divisors of x. Find the smallest possible value of pd(x) for composite x of the form x=n^100+n^99+...+n+1, where n is a positive integer.
It is a very typical question. after solving for a long time, i come at the same point...
I m not sure about its proof but sending example according to this statement.
Example : Factors of 273 = 13 * 7 * 3
In these factors 13 and 7 are prime numbers
So pd(273) = 13 - 7 = 6
This would help you better Finding Factors of Numbers