MathDB

For any natural number, let's call the numbers formed from its digits and have the same "digit" arrangement with the initial number as the "partial numbers". For example, the partial numbers of

149

are

{1, 4, 9, 14,19, 49, 149},

and the partial numbers of

313

are

{3, 1, 31,33, 13, 313}.

Find all natural numbers whose partial numbers are all prime. Justify your opinion.

Problem Statement