Problem of the Week

Note: Because of the fall break, this problem will remain posted for two week.

Two math students, Samantha and Paul, are playing a game.  They put the integers 2, 3,..., 20 into a hat.  A third student reaches into the hat and pulls out two of the numbers at random, tells Samantha the sum and Paul the product of the numbers.  They then try to deduce the integers chosen.  The following conversation takes place:

Samantha:  I know that you don't know the numbers.

Paul:  Hmmm.  Now I know the numbers.

Samantha:  Hmmm.  Now I do, too.

What are the numbers?

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