N is an 11-digit base ten prime number N (with no leading zero) with the proviso that N contains each of the digits from 0 to 9 *at least once*.

Determine the respective minimum and maximum value of N.

I think the minimum is 10,123,457,689.

I started by building a file of all primes < 1,000,000, which is enough to check primality for any 11-digit number. Then running a program with some optimization techniques I was able to get the above number.

Now to work on the maximum ...