Puzzle #22: Mystery Number

There is a unique four-digit number identified by the following clues. What is the number?

  1. Neither 0 nor 8 is a digit.
  2. The mystery number is prime.
  3. The odd digits are not adjacent in the mystery number.
  4. No digits are prime.
  5. Two of the digits are even, and two of them are odd.
  6. All of the digits are different.

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, November 6, 2013 at noon Pacific Time. I will post the answer shortly after.