There is a unique four-digit number identified by the following clues. What is the number?
- Neither 0 nor 8 is a digit.
- The mystery number is prime.
- The odd digits are not adjacent in the mystery number.
- No digits are prime.
- Two of the digits are even, and two of them are odd.
- All of the digits are different.
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, November 6, 2013 at noon Pacific Time. I will post the answer shortly after.