I am thinking of a number between 1 and 5000. It is the product of two primes. I tell my brother the larger of those primes, and to my sister the smaller.
You are allowed to ask each of us questions, first to my brother, then to me, then to my sister, and so on in turns, which we will always respond truthfully and honestly. Our answers will only be "Yes", "No", or "I don't know".
At most how many questions do you need to guess correctly the number I am thinking of?