You have some marbles, each one of the colours red, orange, yellow, green, blue, and violet. There is at least one and no more than nine of each colour. No two colours have the same number of marbles. How many marbles of each colour do you have given the following clues? [Note: 1 is not a prime!]
1) Is there a colour with more marbles than violet has? If so, the number of yellow marbles is prime.
2) The total number of marbles of all colours is even.
3) The number of violet marbles is the product of the number of green marbles and the number of yellow marbles.
4) The number of blue marbles is not prime.
5) The number of red marbles is not prime, the number of green marbles is not prime, but the sum of these is prime and is the number of marbles that are of some other colour.
Submit your answer to Gene Wirchenko <email@example.com>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, December 6, 2017 at noon Pacific Time. I will post the answer shortly after.