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What is the smallest prime that is the sum of three different composite numbers?

 Jun 14, 2020
 #1
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Let's start by listing composite numbers:

 

4, 6, 8, 9, 10, 12, 14, 15, 16, ...

4 + 6 + 8 cannot be prime, but 4 + 6 + 9 can.

 

Also, 19 = 4 + 6 + 9, so the sum is indeed a prime, and the numbers are composite.

 

The required answer is 19.

 Jun 14, 2020

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