Question 234489
The length of each side of triangle ABC is a prime number. Its
perimeter is also a prime number. Find the smallest possible perimeter.


Since a prime number is any integer greater than 1, and the smallest prime number is 2, neither a side of the triangle nor its perimeter will be less than 2.


If we include 2 as a side of the triangle, we will not get a prime number but an even number instead, as, 2 odds added to an even will give us an even, which would give us a composite number.
Therefore, only 3 odd prime integers will add up to a prime number.


Now, let's list a few lower prime numbers, excluding 2. These are: 3, 5, 7, 11, 13


It obviously looks like we can use 3, 3, and 5, as these add up to 11, another 
prime number.


Therefore, our side values are {{{highlight_green(3_3_and_5)}}}, which makes the smallest possible prime perimeter: {{{highlight_green(11)}}} (3 + 3 + 5)