- you drill through as many 0's on the right.

- you finish on 1.

3, 5, 7, 11, 13, 15, 17 are all right truncatable, 19 is the first non-truncatable prime in this scheme.

1. An RTP must start with {2,3,5,7,9}; and,

2. An RTP must end with {1,3,7,9}.

So, let's take the largest RTP (73939133) and try to "extend" it: there are only four possible extensions: 73939133[1], 73939133[3], 73939133[7], 73939133[9]. None of these are prime. This holds for the other 8-digit RTPs. Therefore, there is no extension to a 9-or-longer RTP. Thus, the list is exhaustive.