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Strange Numbers

All strange numbers are prime. Every one digit prime number is strange and a number of two or more digits is strange if and only if so are the two numbers obtained from it by omitting either its first or its last digit. Find all strange numbers.

Weekly Problem 24 - 2006

Stage: 2 and 3 Challenge Level: Challenge Level:1

How many of the three digit numbers that can be made from all of the the digits 1, 3 and 5 (used only once each) are prime?
 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
  

This problem is taken from the UKMT Mathematical Challenges.

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