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# Never Prime

##### Age 14 to 16Challenge Level

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?