Phoebe plays the lottery every week and also plays the same numbers every week as advised by her psychic, who had also predicted that she would be killed by a pigeon. (But that's beside the point!) Phoebe has always been very superstitious as a person and is extremely wary of prime numbers. She says that while she and her sister were growing up, her mom had killed herself on a day when the date was a prime number! Now, in order to win the lottery, a player has to choose six integers between 1 and 49 (1 and 49 are both included!). However, because of her "Prime Number Phobia" (or should we say Phoebia!), she chooses her numbers such that:
1. All six numbers are composite.
2. All of the digits in the six numbers are non-prime.
3. The differences between any two of the six numbers are always composite.
Using the given data, figure out the combination of numbers that she always plays. Provide a detailed explanation along with your answer.