Puzzle #109: Little, Green Apples

There are some apples in a bowl. All of the apples are little, green, or both. There are twice as many little apples as green apples. There are exactly three apples that are both little and green.

The following numbers are not prime: the number of green apples, the number of little apples, the number of green apples that are not little, and the number of little apples that are not green.

What is the minimum number of apples that could be in the bowl?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, July 8, 2015 at noon Pacific Time. I will post the answer shortly after.