Your backyard is covered in snow. There are abcdef snowflakes.
1) abcd is prime.
2) Three of the digit values are odd, and three are even.
3) One digit value is the product of a prime value and a prime value.
4) a ≥ b, c ≥ d, and e ≥ f.
5) All four single-digit primes occur as digit values.
6) b < c < e.
7) All of the digit values are different except for one pair.
8) a < d < f.
So how many snowflakes are there?
Submit your answer to Gene Wirchenko <firstname.lastname@example.org>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, January 14, 2015 at noon Pacific Time. I will post the answer shortly after.