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## 'Never Prime' printed from http://nrich.maths.org/

Take any two digit number, reverse its digits, and subtract the
smaller number from the larger. For example $$42-24=18$$ I've tried
this a few times and I never seem to end up with a prime number.
Try some examples of your own. Do you ever end up with a prime
number?

Can you prove that you will

never end up with a prime?

What happens when I do the same with a three digit number?

What about a four digit number?

What about a five, six, seven, ... $n$ digit number?

Can you justify your findings?