after some discussion me and my friend Bart (well, actually my friend Bart
did the thinking and I did the typing) we came to the following conclusion.
At the end there is the original explanation in Dutch, but I'll try (try!)
to explain it completely in English... here we go:

Part one;

If S says that he knows that P can't determine the numbers, although P
knows their product, this means that the two numbers cannot both be prime
(prime number: number that can only be devided by itself and by 1) .
Because if so, then the product will be reducable to two factors and P
would have known the answer.
This means that the sum S cannot be written as the sum of two prime numbers
(because then S could not be sure of his solution

After this calculation we get a set A of numbers (about 82 i believe)
Because of the confession of S, P now knows that the sum of the possible
factors of the product should be a number in set A.
If P says that he knows it, this indicates that his number (the product P),
can only be factorised in one way in and this sum should be part of set A.
52 can be factorised as 2x26 and 4x13 which respectively gives as sums 28
and 17. Since the sum needs to be part of set A, he knows that his product
should be factorised as 4 and 13.

Part two:

 Now S knows that P knows it for sure, S knows now that: the product P
should be factorisable in one way and their sum  should be part of set A
2+15 (product is 30) can be factorised as

2 * 15 (sum= 17)
3 * 10 (sum= 13)
5 * 6  (sum= 11)

there you go!