A said, "I don't know these two numbers, and neither do you."

B said, "I see."

A said, "I know, too."

Find these two numbers.

Consider the sum of two numbers.

If it can be divided into prime numbers greater than 53 plus a number, or the sum of two prime numbers, it cannot be used as the sum of two numbers.

So the only possible sums are 1 1, 17, 23, 27, 29, 35, 37, 4 1, 47, 5 1.

Logical verification 17=4+ 13 satisfies the condition.