# Thursday Code Puzzler: Pandigital Primes

It's Thursday, so it's time for another code puzzler. The idea is simple: solve the coding problem as efficiently as you can, in any language or framework that you find suitable.

*Note: Even though there really is nothing stopping you from finding a solution to this on the internet, try to keep honest, and come up with your own answer. It's all about the participation!*

**Pandigital Primes **

This weeks task is to find the largest pandigital prime. A number is pandigital if it uses all the digits from 1 to n exactly once. An example would be 123 with is a 3 digit pandigital number.

But here the task is to find the largest n-digits prime that exists.

Catch up on all our previous puzzlers here

## Comments

## sun east replied on Thu, 2013/06/27 - 7:20am

Sine all 8 digit and 9 digit pandigital numbers are divisible by 9, we only to find it from 7654321.

Here it is:

## Fabien Lamarque replied on Thu, 2013/06/27 - 8:38am in response to: sun east

I.... I don't get it. Why would 8 and 9 digits pandigital numbers would be divisible by 9?

## David Whatever replied on Thu, 2013/06/27 - 12:18pm in response to: Fabien Lamarque

There is a cheat for determining division by 9; if all the sum of the digits are divisible by 9, the number itself will be.

1..8 summed is 36, 1..9 is 45 - so all numbers composed of those digits would be divisible by 9

## Frédéric Vergez replied on Sat, 2013/06/29 - 1:30am

Haskell:

## Frédéric Vergez replied on Sat, 2013/06/29 - 1:32am in response to: Frédéric Vergez

Replying to myself to give a sample answer (showing there's only pandigital primes for "order" 1, 4 and 7):

## Rafael Naufal replied on Mon, 2013/07/01 - 1:48pm

## Mark Fisher replied on Wed, 2013/07/03 - 9:20am in response to: David Whatever

Excellent observation. It actually extends to "divisible by 3" too (e.g. 123 sum = 6, which divides by 3).

So we can ignore lengths of: 2 (sum 3), 3 (sum 6), 5 (sum 15), 6 (sum 21), 8 (sum 36) and 9 (sum 45), leaving only lengths 4 and 7 as shown in the results by Frédéric Vergez. (1 is not a prime number, see http://primes.utm.edu/notes/faq/one.html)

## John Schudy replied on Wed, 2013/07/03 - 2:34pm in response to: David Whatever

By the same token, 2, 3, 5, 6 won't have pandigital primes either. (The same rule works for testing divisibility by 3.)

Sorry, I didn't see the other post.

## Bob Beechey replied on Thu, 2013/07/04 - 10:20am

A Python readable version: