Sum and Product Puzzle

X and Y are two integers.

X < Y
X > 1
Y > 1
X + Y < 100

S and P are two perfect logicians. S knows X + Y, and P knows X × Y.

Everything I’ve just said is common knowledge. S and P have the following conversation:

S: “P, you don’t know X and Y”
P: “Now I do know X and Y!”
S: “And now so do I!”

What are X and Y?

Once you figure out that, here’s a question: If instead of saying that X + Y < 100, we say X + Y < N, then what’s the range of values of N for which this puzzle has a unique solution?

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