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 <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, January 14, 2015 at noon Pacific Time.** I will post the answer shortly after.