Rodolfo Kurchan recently asked to me the following question:

"What is the smallest number not dividing any 10 digits-pandigital?"

After I solved his question I asked to him in return:

"What is the smallest prime number not dividing any 10 digits-pandigital?"

Q1. Can you solve both questions without considering an exhaustive test of all the pandigital numbers?

Q2. Redo the exercise with the 9-digits pandigital (zero-free) numbers?

Solution:

Faride Firoozbakht and Patrick de Geest sent contributions to this puzzle.

Faride solved the Kurchan's original question for pandigital numbers the 10 digits and for zero-free pandigital  numbers of 9 digits: 100 and 10, respectively.

Faride and Patrick de Geest found the prime-solutions to the Rivera's question but not satisfying the condition of the puzzle (not testing ALL the pandigitals in any case). So I will not show them yet.

***