A prime butterfly is a set of three distinct numbers $a,b,c$, such that $a+b$ and $b+c$ are both primes. Can you divide numbers from 1 to 30 into 10 prime butterflies?
First, observe the facts that:
Each triplet must be either an Even-Odd-Odd triplet, or an Odd-Even-Even triplet. Now there are 15 Odd and 15 Even numbers between 1 and 30. Hence, there will be 15 triplets of Even-Odd-Odd combination, and another 15 of Odd-Even-Even combination. After this, I started putting the first 5 even numbers (one in each triplet) to populate the first 5 triplets.
Proceeding further, the final answer is then: