Strange Numbers

We define "strange" numbers in the following way:

• All strange numbers are prime.
   
• Every single digit prime number is strange. 
   
• A number with two or more digits is strange if, and only if, the two numbers obtained from it, by removing either its first or its last digit, are also strange.

Find all strange numbers.

This problem comes from the Hungarian magazine KoMaL. You can find many other challenging problems in English on the KoMaL website.