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Hello Sam,
I can't follow your reasoning but I am quiet sure it can't be 3 and 4 because in that case the person with the sum is not able to reply with "i know that you don't know the two numbers"; he would get 7 (3+4). From his perspection the numbers could then be 3+4 or 2+5 in the case of 2+5, the person with the product has 10 and should be able to know the combination as 10 can only be made out of 2x5 (both 2 and 5 are prime numbers).
Best regards,
Ronald
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