There is a city of wise men.
Once, a clairvoyant came, summoned all the men in the square and said: "In this town there is at least one unfaithful wife. Whoever of you finds out that his wife is unfaithful, write her name on the blackboard at the church during the night, so that her shame serves as an example for others. "
Sages thoughtfully returned to their homes. Everyone knows about all other women, whether they are faithful or not... but noone knows about his own wife. They are proud of their wisdom, so they won't tell each other.
Exactly a week later, there were names of all the unfaithful women on the blackboard.
Write comma separated numbers of names at the blackboard after the first, second... up to seventh night.
There are two natural numbers greater than one, whose sum is less than 100.
And there are two friends: Peter, who knows the product of the numbers, and Paul, who knows their sum.
A following dialogue takes place:
Peter: "I don't know those numbers."
Paul: "I knew you wouldn't. I don't know them either."
Peter: "Now I know them!"
Paul: "Now I know them, too!"
What are those two numbers?