[College Number Theory] (Repost with full prompt) Find N

Any and all help! I’m kind of stumped:

The goal is to find the smallest number (let's call it **N**) such that:

* If N obeys property X, then the digit X is part of the number. * If N does not obey property X, then the digit X is NOT part of the number.

For example, if 2457 were a magic number, it would obey properties 2, 4, 5, 7 and not 0, 1, 3, 6, 8, 9. However we find that not to be the case, so it is not the number we are looking for.

## Properties

* **0**. One of the digits of N is the sum of the others. * **1**. Digits in decreasing sequence. * **2**. M has at least 2 odd digits. * **3**. All digits are different. * **4**. There is no subset in the digits with a sum of 4. * **5**. The number is not a palindrome. * **6**. The number does not contain 3 odd digits in a row. * **7**. N is a prime number. * **8**. N has at least 2 even digits in a row. * **9**. The product of all odd digits is a square number.

Edit: Format

I think it’s maybe 6