In my prime

The key is that a multiple of 3 always has figures that add up to another multiple of 3. No matter the arrangement, the sum of the digits is always 45 (0+1+2+3+4+5+6+7+8+9=45) Hence any number created will be a multiple of 3 and therefor can't be a prime.

There can't be one. You see, any number whose sum of individual digits is divisible by 3, can be divided by 3. And the sum from 1 through 9 is 45. 45 is clearly divisible by 3 which means that there can't exist such a prime number with your given condition.

1+2+3+...+9=45

so any such number will be always divisible by 3, 9 etc

hence can't be a prime.