Mr. Sum and Mr. Product

a and b are integers greater than 1.
Mr. Sum knows only their sum (a+b).
Mr. Product knows only their product (a*b),
Statement 1: Mr. Sum says to Mr. Product "I know you don't know what a and b are".
Statement 2: Mr. Product says to Mr. Sum "Now I know what a and b are".
Statement 3: Mr. Sum says "Now I know what a and b are".
What are a and b?
This page works out if a particular sum yields a value of a and b consistent with all three statements.