Sum and Product Puzzle

X and Y are two different whole numbers greater than 1 and less then 100, and Y is greater than X. S and P are two mathematicians (and consequently perfect logicians); S knows the sum X + Y and P knows the product X * Y. Both S and P know all the information in this paragraph.

The following conversation occurs:

P says "I don't know X and Y."
S says "I know you don't know X and Y."
P says "Now I know X and Y."
S says "Now I also know X and Y."

What are X and Y? (type in the product)

It might be interesting to see methods of solving this puzzle, since the correct answer is just a google away.