You had some marbles each of one colour of red, orange, yellow, green, blue, and violet, but you lost some of them. Fortunately, you did not lose all of your marbles.
First, you lost two of each colour. Then, you lost three each of red, yellow, and violet. Then, you lost two each of green, blue, and violet. You now have a prime number of marbles of each colour and all of these numbers are different, and the number of marbles you have now is the lowest number it can be. What is the maximum number of marbles you could have had before your losses?
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, October 7, 2015 at noon Pacific Time. I will post the answer shortly after.