In what base(s) there exist a prime number abcd (a string of distinct digits), such that a, ab, abc are also prime numbers?

(In reply to computer solution by Charlie)

There is no base lower than 7 with  matryoshkas with distinct digits.

7      2564  2 19 139 977     is the 1st valid entry

The long list definitely needs revision.

 I suggest reducing the output to include only the minimal and maximal values (distinct digits only) for all bases below 24(a reasonable choice) or other number of your choice.

I understand 36 was chosen not to exceed the letters of the English ABC, but 16, 20 or 24 will do as well.

Edited on March 3, 2016, 7:39 pm

Posted by Ady TZIDON on 2016-03-03 19:07:08