Choose any non-prime number N, and then choose two of its factor pairs.

For example, if we choose 20, we may take the factor pairs (4,5) and (2,10).

Now add all of these factors together (for this example this would be 4 + 5 + 2 + 10 = 21).

Find an example for which this sum is prime... or explain why it is not possible.

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If you would like a hint, here is a video I made which may give some insight.