This is definitely one of the harder number puzzles on this site.

A teacher says: I'm thinking of two natural numbers greater than 1. Try to guess what they are.

The first student knows their product and the other one knows their sum.

First: I do not know the sum.

Second: I knew that. The sum is less than 14.

First: I knew that. However, now I know the numbers.

Second: And so do I.

**What were the numbers?**