# The first 10 prime butterflies

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?

## 1 Answer

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:

• Maybe fix the headings in the right hand table to "odd even even" – theonetruepath Nov 7 '19 at 23:58
• Sorry..changed now – SamRoy Nov 8 '19 at 0:02
• Correct! Well done. – Dmitry Kamenetsky Nov 8 '19 at 0:52