Pandigitial primes

I got a fun little question from Jean-Marie by email the other day. With the disclaimer that I don’t really have the time to solve that many puzzles and therefore probably wont be able to give you a solution to puzzles like this one. This one triggered my curiosity and I managed to find a rather cure solution.

Therefore I will post it to you all and let you wonder a bit about it. If you find the solution feel free to post it in the comments.

The question is simple:

Find all the primes that contain 9 different digits (0 excluded).

Good luck 🙂

Posted by Kristian

Bjarki Ágúst

Haha. Good one!

```Since 1+2+...+9 = 45 is divisible by 3, all (1-9) pandigital
numbers are divisible by 3. And therefore none of them are prime.
```
Jean-Marie Hachey

… and the biggest prime with 9 different digits (excluding 2) is …

987654103
The largest prime number of 9 different digits.

___

Note :
987654301 :
987654301 has the following properties:
It is composite and has the factorization: 2029×486769
http://www.mathblog.dk/tools/prime-factorization/

Jean-Marie Hachey

More on the subject …

Sum of digits and divisibility by 3
http://eli.thegreenplace.net/2006/07/11/sum-of-digits-and-divisibility-by-3/

and the references cited therein.