B said, I don't know what those two numbers are.

That means that the sum of those two numbers is not 3 or 4, and if it is, it is guessed;

C said: You don't know and I don't know.

In other words, the product of those two numbers is not 2, 3, 4, 5, 7 ... (prime number). Otherwise, C wouldn't say so;

B thought for a moment and said, then I know what those two numbers are.

B can guess, which means that he ruled out some possibilities he drew through C's words and left a set of unique answers. And C's answer can only rule out one possibility for B, indicating that B's guess can only be two kinds, and only 5 and 6 can be split into two kinds (for example, 7, he may be 1+6, 2+5, 3+4, three kinds).

If the sum is 5, it can be divided into 1+4 or 2+3. If it is 1+4, the product is 4, and C says that the product is not 4, so 1+4 doesn't hold, so those two numbers are 2 and 3.

Similarly, 6 can be divided into 1+5 or 2+4, because the product cannot be 5, so those two numbers can only be 2 and 4.

To sum up, A and B should be 2 and 3 or 2 and 4.